A348350 - OEIS

%I #15 Oct 15 2021 08:38:33

%S 1,5,28,4101,3126,362797088,823544,4398046515205,282429536509,

%T 100000000000003130,285311670612,137370551967459378662949775392,

%U 302875106592254,229585692886981495483044092,1122274146401882171630862528

%N a(n) = Sum_{d|n} d^(sigma(d) - 1).

%F G.f.: Sum_{k>=1} k^(sigma(k) - 1) * x^k/(1 - x^k).

%F If p is prime, a(p) = 1 + p^p.

%t a[n_] := DivisorSum[n, #^(DivisorSigma[1, #] - 1) &]; Array[a, 14] (* _Amiram Eldar_, Oct 14 2021 *)

%o (PARI) a(n) = sumdiv(n, d, d^(sigma(d)-1));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(sigma(k)-1)*x^k/(1-x^k)))

%Y Cf. A000203, A174472, A347991, A348223, A348349.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Oct 14 2021