A344080 a(n) = Sum_{d|n} tau(d)^n, where tau(n) is the number of divisors of n.
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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..719
Programs
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Mathematica
a[n_] := DivisorSum[n, DivisorSigma[0, #]^n &]; Array[a, 26] (* Amiram Eldar, May 09 2021 *)
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PARI
a(n) = sumdiv(n, d, numdiv(d)^n);
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (numdiv(k)*x)^k/(1-(numdiv(k)*x)^k)))
Formula
G.f.: Sum_{k >= 1} (tau(k) * x)^k/(1 - (tau(k) * x)^k).
If p is prime, a(p) = 1 + 2^p.