A347991 a(n) = Sum_{d|n} 2^(sigma(d) - 1).

1, 5, 9, 69, 33, 2061, 129, 16453, 4105, 131109, 2049, 134219853, 8193, 8388741, 8388649, 1073758277, 131073, 274877913101, 524289, 2199023386725, 2147483785, 34359740421, 8388609, 576460752437659725, 1073741857, 2199023263749, 549755817993, 36028797027352773, 536870913, 2361183241434831128621

Offset: 1

Author

Seiichi Manyama, Oct 08 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A347405, A348223.

Programs

Mathematica

a[n_] := DivisorSum[n, 2^(DivisorSigma[1, #] - 1) &]; Array[a, 30] (* Amiram Eldar, Oct 08 2021 *)

PARI

a(n) = sumdiv(n, d, 2^(sigma(d)-1));

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, 2^(sigma(k)-1)*x^k/(1-x^k)))

Formula

If p is prime, a(p) = 1 + 2^p.

G.f.: Sum_{k>=1} 2^(sigma(k) - 1) * x^k/(1 - x^k).