A369903 a(n) = Sum_{p|n, p prime} n^sigma(n/p).

0, 2, 3, 64, 5, 1512, 7, 2097152, 6561, 1001000, 11, 8916136280064, 13, 1475791800, 11441250, 1152921504606846976, 17, 21979796247097344, 19, 262144000000001280000000, 37823053842, 12855002631059864, 23, 442501521100279866178075737690262732800, 244140625

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

a(p^k) = p^(k*(1-p^k)/(1-p)), for prime p and k >= 1. - Wesley Ivan Hurt, Jun 26 2024

Mathematica

Table[DivisorSum[n, n^DivisorSigma[1, n/#] &, PrimeQ[#] &], {n, 30}]

Crossrefs

Cf. A000203 (sigma), A323599, A329354, A369740.

Sequence in context: A293041 A284755 A061452 * A280582 A037426 A004854

Adjacent sequences: A369900 A369901 A369902 * A369904 A369905 A369906

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved