OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
If p is prime, a(p^n) = 2^(n+1) - 1.
G.f.: Sum_{k>=1} 2^(tau(k) - 1) * x^k/(1 - x^k).
MATHEMATICA
a[n_] := DivisorSum[n, 2^(DivisorSigma[0, #] - 1) &]; Array[a, 80] (* Amiram Eldar, Oct 08 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, 2^(numdiv(d)-1));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 2^(numdiv(k)-1)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 08 2021
STATUS
approved