OFFSET
1,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n^8 * Sum_{d|n, d<n, d odd} 1 / d^8.
G.f.: Sum_{k>=2} k^8 * x^k / (1 - x^(2*k)). - Ilya Gutkovskiy, May 19 2023
From Amiram Eldar, Oct 13 2023: (Start)
Sum_{k=1..n} a(k) = c * n^9 / 9, where c = 511*zeta(9)/512 = 1.0000513451... . (End)
EXAMPLE
a(10) = 10^8 * Sum_{d|10, d<10, d odd} 1 / d^8 = 10^8 * (1/1^8 + 1/5^8) = 100000256.
MATHEMATICA
A352054[n_]:=DivisorSum[n, 1/#^8&, #<n&&OddQ[#]&]n^8; Array[A352054, 50] (* Paolo Xausa, Aug 09 2023 *)
a[n_] := DivisorSigma[-8, n/2^IntegerExponent[n, 2]] * n^8 - Mod[n, 2]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
PROG
(PARI) a(n) = n^8 * sigma(n >> valuation(n, 2), -8) - n % 2; \\ Amiram Eldar, Oct 13 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 01 2022
STATUS
approved