OFFSET
1,2
COMMENTS
Here tau(n) = A000005(n) = the number of divisors of n.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
Logarithmic derivative of A174473.
G.f.: Sum_{k>=1} k^tau(k) * x^k/(1 - x^k). - Seiichi Manyama, Oct 14 2021
EXAMPLE
For n = 4, A007955(n) = b(n): a(4) = b(1)^2 + b(2)^2 + b(4)^2 = 1^2 + 2^2 + 8^2 = 69.
MATHEMATICA
a[n_] := DivisorSum[n, #^DivisorSigma[0, #] &]; Array[a, 30] (* Amiram Eldar, Oct 08 2021 *)
PROG
(PARI) {a(n)=sumdiv(n, d, d^sigma(d, 0))}
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k^numdiv(k)*x^k/(1-x^k))) \\ Seiichi Manyama, Oct 14 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek and Paul D. Hanna, Apr 02 2010
STATUS
approved