A110566 -id:A110566 - cp's OEIS frontend

A120263 Ratio of the numerator of n*HarmonicNumber[n] to the numerator of HarmonicNumber[n]: A096617(n)/A001008(n).

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1

Offset: 1

Alexander Adamchuk, Jun 26 2006

a(n) is not equal to 1 when n belongs to A074791 - numbers n such that n does not divide the denominator of the n-th harmonic number.
a(n) is almost always equal to 1 except for n=6,18,20,21,33,42,54,.. when a(n) seems to be equal to a prime divisor of n.
a(n) could be equal to a squared prime divisor of n as for n=100,294,500,847,..

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A096617, A001008, A074791.

[Numerator(n*HarmonicNumber(n))/Numerator(HarmonicNumber(n)): n in [1..100]]; // G. C. Greubel, Sep 01 2018

Numerator[Table[n*Sum[1/i,{i,1,n}],{n,1,500}]]/Numerator[Table[Sum[1/i,{i,1,n}],{n,1,500}]]

{h(n) = sum(k=1,n,1/k)};
for(n=1,100, print1(numerator(n*h(n))/numerator(h(n)), ", ")) \\ G. C. Greubel, Sep 01 2018

a(n) = A096617(n)/A001008(n) = numerator[n*Sum[1/i,{i,1,n}]] / numerator[Sum[1/i,{i,1,n}]].
a(n) = n / gcd(denominator(H(n)),n), where H(n) = sum(1/k, k=1..n). [Gary Detlefs, Sep 05 2011]
a(n) = A096617(n)*A110566(n)/A025529(n). [Arkadiusz Wesolowski, Mar 29 2012]

A269626 a(n) = A003418(n) / A058312(n) with a(0) = 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 55, 55, 55, 55, 55, 55, 55

Offset: 0

Jeppe Stig Nielsen, Mar 01 2016

nonn

Cf. A003418, A058312, A110566.

a(n)=lcm([1..n])/denominator(sum(k=1,n,(-1)^(k+1)/k))

A342351 Numbers k such that lcm(1,2,3,...,k)/23 equals the denominator of the k-th harmonic number H(k).

Original entry on oeis.org

11881, 11882, 11883, 11884, 11885, 11886, 11887, 11888, 11889, 11890, 11891, 11892, 11893, 11894, 11895, 11896, 11897, 11898, 11899, 11900, 11901, 11902, 11903, 11904, 11905, 11906, 11907, 11908, 11909, 11910, 11911, 11912, 11913, 11914, 11915, 11916, 11917

Offset: 1

Chai Wah Wu, Mar 17 2021

nonn

Positions where 23 occurs in A110566.

Chai Wah Wu, Table of n, a(n) for n = 1..9014
Tanya Khovanova, Non Recursions

Cf. A002805, A003418, A110566.

Cf. A098464, A112813, A112814, A112815, A112816, A112817, A112818, A112819, A112820, A112821, A112822, A342350.

cp's OEIS Frontend

A120263 Ratio of the numerator of n*HarmonicNumber[n] to the numerator of HarmonicNumber[n]: A096617(n)/A001008(n).

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A269626 a(n) = A003418(n) / A058312(n) with a(0) = 1.

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A342351 Numbers k such that lcm(1,2,3,...,k)/23 equals the denominator of the k-th harmonic number H(k).

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