調和数と一般化調和数の間には
\[ H_{n,1}=H_{n} \] の関係がある。

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調和数と一般化調和数の一覧
\[ \begin{array}{|c|c|c|c|c|c|} \hline n & H_{n} & H_{n,2} & H_{n,3} & H_{n,4} & H_{n,5}\\ \hline 1 & 1 & 1 & 1 & 1 & 1\\ \hline 2 & \frac{3}{2} & \frac{5}{4} & \frac{9}{8} & \frac{17}{16} & \frac{33}{32}\\ \hline 3 & \frac{11}{6} & \frac{49}{36} & \frac{251}{216} & \frac{1,393}{1,296} & \frac{8,051}{7,776}\\ \hline 4 & \frac{25}{12} & \frac{205}{144} & \frac{2,035}{1,728} & \frac{22,369}{20,736} & \frac{257,875}{248,832}\\ \hline 5 & \frac{137}{60} & \frac{5,269}{3,600} & \frac{256,103}{216,000} & \frac{14,001,361}{12,960,000} & \frac{806,108,207}{777,600,000}\\ \hline 6 & \frac{49}{20} & \frac{5,369}{3,600} & \frac{28,567}{24,000} & \frac{14,011,361}{12,960,000} & \frac{268,736,069}{259,200,000}\\ \hline 7 & \frac{363}{140} & \frac{266,681}{176,400} & \frac{9,822,481}{8,232,000} & \frac{33,654,237,761}{31,116,960,000} & \frac{4,516,906,311,683}{4,356,374,400,000}\\ \hline 8 & \frac{761}{280} & \frac{1,077,749}{705,600} & \frac{78,708,473}{65,856,000} & \frac{538,589,354,801}{497,871,360,000} & \frac{144,545,256,245,731}{139,403,980,800,000}\\ \hline 9 & \frac{7,129}{2,520} & \frac{9,778,141}{6,350,400} & \frac{19,148,110,939}{16,003,008,000} & \frac{43,631,884,298,881}{40,327,580,160,000} & \frac{105,375,212,839,937,899}{101,625,502,003,200,000}\\ \hline 10 & \frac{7,381}{2,520} & \frac{1,968,329}{1,270,080} & \frac{19,164,113,947}{16,003,008,000} & \frac{43,635,917,056,897}{40,327,580,160,000} & \frac{105,376,229,094,957,931}{101,625,502,003,200,000}\\ \hline 11 & \frac{83,711}{27,720} & \frac{239,437,889}{153,679,680} & \frac{25,523,438,671,457}{21,300,003,648,000} & \frac{638,913,789,210,188,977}{590,436,101,122,560,000} & \frac{16,971,048,697,474,072,945,481}{16,366,888,723,117,363,200,000}\\ \hline 12 & \frac{86,021}{27,720} & \frac{240,505,109}{153,679,680} & \frac{25,535,765,062,457}{21,300,003,648,000} & \frac{638,942,263,173,398,977}{590,436,101,122,560,000} & \frac{16,971,114,472,329,088,045,481}{16,366,888,723,117,363,200,000}\\ \hline 13 & \frac{1,145,993}{360,360} & \frac{40,799,043,101}{25,971,865,920} & \frac{56,123,375,845,866,029}{46,796,108,014,656,000} & \frac{18,249,420,414,596,570,742,097}{16,863,445,484,161,436,160,000} & \frac{6,301,272,372,663,207,205,033,976,933}{6,076,911,214,672,415,134,617,600,000}\\ \hline 14 & \frac{1,171,733}{360,360} & \frac{40,931,552,621}{25,971,865,920} & \frac{56,140,429,821,090,029}{46,796,108,014,656,000} & \frac{18,249,859,383,918,836,502,097}{16,863,445,484,161,436,160,000} & \frac{6,301,283,671,733,562,325,696,376,933}{6,076,911,214,672,415,134,617,600,000}\\ \hline 15 & \frac{1,195,757}{360,360} & \frac{205,234,915,681}{129,859,329,600} & \frac{56,154,295,334,575,853}{46,796,108,014,656,000} & \frac{18,250,192,489,014,819,937,873}{16,863,445,484,161,436,160,000} & \frac{6,301,291,674,250,388,231,757,459,557}{6,076,911,214,672,415,134,617,600,000}\\ \hline 16 & \frac{2,436,559}{720,720} & \frac{822,968,714,749}{519,437,318,400} & \frac{449,325,761,325,072,949}{374,368,864,117,248,000} & \frac{292,007,196,876,357,275,606,593}{269,815,127,746,582,978,560,000} & \frac{201,641,519,028,625,175,870,313,858,949}{194,461,158,869,517,284,307,763,200,000}\\ \hline 17 & \frac{42,142,223}{12,252,240} & \frac{238,357,395,880,861}{150,117,385,017,600} & \frac{2,207,911,834,254,200,646,437}{1,839,274,229,408,039,424,000} & \frac{24,389,002,905,437,982,598,916,813,953}{22,535,229,284,522,356,952,309,760,000} & \frac{286,302,316,744,585,525,852,980,532,588,950,293}{276,107,037,648,996,202,745,367,733,862,400,000}\\ \hline 18 & \frac{14,274,301}{4,084,080} & \frac{238,820,721,143,261}{150,117,385,017,600} & \frac{245,358,578,943,756,786,493}{204,363,803,267,559,936,000} & \frac{24,389,217,575,736,760,627,770,573,953}{22,535,229,284,522,356,952,309,760,000} & \frac{95,434,154,288,788,166,027,220,236,648,583,431}{92,035,679,216,332,067,581,789,244,620,800,000}\\ \hline 19 & \frac{275,295,799}{77,597,520} & \frac{86,364,397,717,734,821}{54,192,375,991,353,600} & \frac{1,683,118,856,778,495,358,491,487}{1,401,731,326,612,193,601,024,000} & \frac{3,178,449,758,916,874,904,128,641,277,888,913}{2,936,813,615,588,238,080,381,960,232,960,000} & \frac{236,304,506,035,993,305,443,901,582,534,565,405,715,669}{227,889,453,271,880,616,207,200,766,816,318,259,200,000}\\ \hline 20 & \frac{55,835,135}{15,519,504} & \frac{17,299,975,731,542,641}{10,838,475,198,270,720} & \frac{336,658,814,638,864,376,538,323}{280,346,265,322,438,720,204,800} & \frac{3,178,468,114,001,972,330,616,643,665,140,369}{2,936,813,615,588,238,080,381,960,232,960,000} & \frac{1,890,436,618,011,579,623,252,753,178,278,440,286,521}{1,823,115,626,175,044,929,657,606,134,530,546,073,600}\\ \hline 21 & \frac{18,858,053}{5,173,168} & \frac{353,562,301,485,889}{221,193,371,393,280} & \frac{336,689,086,344,438,551,975,123}{280,346,265,322,438,720,204,800} & \frac{454,069,030,682,272,428,425,792,500,185,767}{419,544,802,226,891,154,340,280,033,280,000} & \frac{1,890,437,064,404,953,875,026,871,805,023,012,600,121}{1,823,115,626,175,044,929,657,606,134,530,546,073,600}\\ \hline 22 & \frac{19,093,197}{5,173,168} & \frac{354,019,312,583,809}{221,193,371,393,280} & \frac{336,715,414,881,752,830,592,723}{280,346,265,322,438,720,204,800} & \frac{454,070,821,649,428,987,451,620,399,065,767}{419,544,802,226,891,154,340,280,033,280,000} & \frac{171,857,947,105,318,724,275,995,454,218,597,556,811}{165,737,784,197,731,357,241,600,557,684,595,097,600}\\ \hline 23 & \frac{444,316,699}{118,982,864} & \frac{187,497,409,728,228,241}{117,011,293,467,045,120} & \frac{4,097,096,799,131,609,128,541,865,541}{3,410,973,010,178,111,908,731,801,600} & \frac{127,068,052,346,000,084,168,603,244,374,996,583,047}{117,405,836,999,975,447,521,738,304,793,108,480,000} & \frac{1,106,136,860,583,472,631,494,090,651,392,248,539,192,679,773}{1,066,745,227,156,578,837,062,475,058,249,339,864,272,076,800}\\ \hline 24 & \frac{1,347,822,955}{356,948,592} & \frac{187,700,554,334,941,861}{117,011,293,467,045,120} & \frac{4,097,343,541,970,887,059,090,818,941}{3,410,973,010,178,111,908,731,801,600} & \frac{127,068,406,216,795,439,997,377,844,521,796,813,047}{117,405,836,999,975,447,521,738,304,793,108,480,000} & \frac{1,106,136,994,552,529,459,567,202,864,461,088,440,378,502,973}{1,066,745,227,156,578,837,062,475,058,249,339,864,272,076,800}\\ \hline 25 & \frac{34,052,522,467}{8,923,714,800} & \frac{23,485,971,550,561,141,649}{14,626,411,683,380,640,000} & \frac{2,560,976,152,652,211,536,408,111,110,189}{2,131,858,131,361,319,942,957,376,000,000} & \frac{79,417,941,734,836,349,959,077,187,607,410,677,127,943}{73,378,648,124,984,654,701,086,440,495,692,800,000,000} & \frac{432,084,806,166,890,906,406,592,101,429,115,001,996,447,294,711,197}{416,697,354,358,038,608,227,529,319,628,648,384,481,280,000,000,000}\\ \hline 26 & \frac{34,395,742,267}{8,923,714,800} & \frac{23,507,608,254,234,781,649}{14,626,411,683,380,640,000} & \frac{2,561,097,446,355,634,460,847,287,110,189}{2,131,858,131,361,319,942,957,376,000,000} & \frac{79,418,102,309,238,780,250,065,556,988,823,477,127,943}{73,378,648,124,984,654,701,086,440,495,692,800,000,000} & \frac{432,084,841,238,363,634,652,765,627,755,469,763,317,727,294,711,197}{416,697,354,358,038,608,227,529,319,628,648,384,481,280,000,000,000}\\ \hline 27 & \frac{312,536,252,003}{80,313,433,200} & \frac{211,749,047,271,858,474,841}{131,637,705,150,425,760,000} & \frac{622,372,998,700,608,819,911,112,463,775,927}{518,041,525,920,800,746,138,642,368,000,000} & \frac{6,432,877,471,112,984,544,967,198,713,326,906,447,363,383}{5,943,670,498,123,757,030,788,001,680,151,116,800,000,000} & \frac{314,989,870,433,185,946,443,790,047,908,813,392,460,827,357,844,462,613}{303,772,371,327,010,145,397,868,874,009,284,672,286,853,120,000,000,000}\\ \hline 28 & \frac{315,404,588,903}{80,313,433,200} & \frac{10,383,930,672,892,966,877,209}{6,450,247,552,370,862,240,000} & \frac{622,396,597,531,053,462,802,244,872,775,927}{518,041,525,920,800,746,138,642,368,000,000} & \frac{45,030,209,987,187,053,027,382,348,764,808,937,231,543,681}{41,605,693,486,866,299,215,516,011,761,057,817,600,000,000} & \frac{314,989,888,083,730,741,709,652,195,532,203,781,863,579,947,844,462,613}{303,772,371,327,010,145,397,868,874,009,284,672,286,853,120,000,000,000}\\ \hline 29 & \frac{9,227,046,511,387}{2,329,089,562,800} & \frac{8,739,335,943,455,356,005,972,769}{5,424,658,191,543,895,143,840,000} & \frac{15,180,148,658,710,783,705,030,088,844,500,083,603}{12,634,514,775,682,409,397,575,348,713,152,000,000} & \frac{31,849,053,555,641,132,918,559,230,532,734,590,991,881,046,241,361}{29,426,916,495,084,282,975,449,380,314,372,734,289,945,600,000,000} & \frac{6,460,804,831,751,097,046,097,336,318,607,040,077,452,058,270,503,121,480,172,337}{6,230,720,370,371,632,816,767,352,757,266,665,296,691,815,085,434,880,000,000,000}\\ \hline 30 & \frac{9,304,682,830,147}{2,329,089,562,800} & \frac{8,745,363,341,445,960,333,910,369}{5,424,658,191,543,895,143,840,000} & \frac{15,180,616,603,702,475,646,118,887,931,489,459,603}{12,634,514,775,682,409,397,575,348,713,152,000,000} & \frac{31,849,089,885,167,670,059,649,323,680,117,695,155,750,540,001,361}{29,426,916,495,084,282,975,449,380,314,372,734,289,945,600,000,000} & \frac{6,460,805,088,159,342,740,403,213,551,831,433,380,607,008,751,647,775,201,772,337}{6,230,720,370,371,632,816,767,352,757,266,665,296,691,815,085,434,880,000,000,000} \\\hline \end{array} \]