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A348350
a(n) = Sum_{d|n} d^(sigma(d) - 1).
1
1, 5, 28, 4101, 3126, 362797088, 823544, 4398046515205, 282429536509, 100000000000003130, 285311670612, 137370551967459378662949775392, 302875106592254, 229585692886981495483044092, 1122274146401882171630862528
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} k^(sigma(k) - 1) * x^k/(1 - x^k).
If p is prime, a(p) = 1 + p^p.
MATHEMATICA
a[n_] := DivisorSum[n, #^(DivisorSigma[1, #] - 1) &]; Array[a, 14] (* Amiram Eldar, Oct 14 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^(sigma(d)-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(sigma(k)-1)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2021
STATUS
approved