OFFSET
1,2
COMMENTS
If p is prime, a(p) = 1 + p^3. - Robert Israel, Nov 03 2017
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..3143
FORMULA
L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 12 2018
G.f.: Sum_{k>0} k^3 * x^k / (1 - k^2 * x^k). - Seiichi Manyama, Jan 14 2023
MAPLE
f:= n -> add(d^(1+2*n/d), d=numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Nov 03 2017
MATHEMATICA
sd[n_] := Module[{d = Divisors[n]}, Total[d^(1 + (2 n)/d)]]; Array[sd, 40] (* Harvey P. Dale, Mar 17 2020 *)
a[n_] := DivisorSum[n, #^(1 + 2*n/#) &]; Array[a, 33] (* Amiram Eldar, Oct 04 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^(1+2*n/d)); \\ Michel Marcus, Nov 02 2017
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k^3*x^k/(1-k^2*x^k))) \\ Seiichi Manyama, Jan 14 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 02 2017
STATUS
approved