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A344080
a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n.
3
1, 5, 9, 98, 33, 4225, 129, 72354, 20196, 1050625, 2049, 2194099186, 8193, 268468225, 1073807361, 156925970179, 131073, 101629064089930, 524289, 3657261440572306, 4398050705409, 17592194433025, 8388609, 4727105427440383342818, 847322163876, 4503599761588225
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k >= 1} (tau(k) * x)^k/(1 - (tau(k) * x)^k).
If p is prime, a(p) = 1 + 2^p.
MATHEMATICA
a[n_] := DivisorSum[n, DivisorSigma[0, #]^n &]; Array[a, 26] (* Amiram Eldar, May 09 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, numdiv(d)^n);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-(numdiv(k)*x)^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 09 2021
STATUS
approved