A103930 -id:A103930 - cp's OEIS frontend

A103931 Denominators of squares of harmonic numbers A001008/A002805.

1, 4, 36, 144, 3600, 400, 19600, 78400, 6350400, 6350400, 768398400, 768398400, 129859329600, 129859329600, 129859329600, 519437318400, 150117385017600, 16679709446400, 6021375110150400, 240855004406016, 26761667156224

Offset: 1

Wolfdieter Lang, Mar 24 2005

The corresponding numerators are given in A103930. For the rational see the link there.

Denominator[HarmonicNumber[Range[30]]^2] (* Harvey P. Dale, Oct 16 2022 *)

a(n)=denominator(H(n)^2), with the harmonic numbers H(n)=A001008(n)/A002805(n), n>=1.

A348373 Decimal expansion of Sum_{k>=1} H(k)^2/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

Original entry on oeis.org

2, 1, 2, 5, 3, 8, 7, 0, 8, 0, 7, 6, 6, 4, 2, 7, 8, 6, 1, 1, 3, 9, 5, 1, 7, 6, 9, 2, 9, 7, 2, 6, 9, 0, 1, 6, 0, 9, 4, 9, 5, 0, 2, 8, 5, 2, 8, 0, 1, 3, 4, 4, 0, 2, 4, 6, 0, 2, 4, 2, 2, 3, 6, 2, 9, 9, 3, 6, 7, 2, 8, 5, 2, 6, 6, 3, 0, 3, 5, 3, 4, 6, 0, 3, 3, 5, 7, 7, 1, 6, 4, 0, 6, 3, 6, 8, 5, 6, 9, 6, 2, 3, 6, 7, 1

Offset: 1

Amiram Eldar, Oct 15 2021

			2.12538708076642786113951769297269016094950285280134...

István Mező, A q-Raabe formula and an integral of the fourth Jacobi theta function, Journal of Number Theory, Vol. 133, No. 2 (2013), pp. 692-704.
Seán Mark Stewart, Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers, Tatra Mountains Mathematical Publications, Vol. 77, No. 1 (2020), pp. 73-98.

Cf. A001008, A002805, A013661, A103930, A103931, A253191.

Similar constants: A016627, A076788.

RealDigits[Pi^2/6 + Log[2]^2, 10, 100][[1]]

Equals Pi^2/6 + log(2)^2 = A013661 + A253191.

cp's OEIS Frontend

A103931 Denominators of squares of harmonic numbers A001008/A002805.

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