A354062 a(n) = Li(-2^n, 1/3), where Li(n, z) is the polylogarithm function.

15, 17295, 4229255279355, 11811493418737804581195936694907475

Offset

2,1

Comments

The next term, a(6) = 2.808...*10^86, is too large to include in the data section.

a(n) is an integer for all n >= 2 (Aloff, 2022).

Conjecture: for k >= 0, a(n) is divisible by 2^2^k+1 = A000215(k) for all n >= 2^max{k,1}. - Jianing Song, May 17 2022

Links

Amiram Eldar, Table of n, a(n) for n = 2..8

Simon Aloff, A Family of Infinite Series Taking Integer Values, Missouri J. Math. Sci., Vol. 34 , No. 1 (2022), pp. 1-18.

Eric Weisstein's World of Mathematics, Polylogarithm.

Wikipedia, Polylogarithm.

Formula

a(n) = Sum_{k>=1} k^2^n/3^k. - Jianing Song, May 17 2022

Mathematica

a[n_] := PolyLog[-2^n, 1/3]; Array[a, 5, 2]

Prog

(PARI) a(n) = polylog(-2^n, 1/3); \\ Michel Marcus, May 16 2022

Crossrefs

Cf. A210246, A212846, A212847, A213127.

Sequence in context: A112614 A238634 A198521 * A212924 A068732 A174304

Adjacent sequences: A354059 A354060 A354061 * A354063 A354064 A354065

Keyword

nonn

Author

Amiram Eldar, May 16 2022

Status

approved