A369905 a(n) = Sum_{p|n, p prime} n^omega(n/p).

0, 1, 1, 4, 1, 12, 1, 8, 9, 20, 1, 156, 1, 28, 30, 16, 1, 342, 1, 420, 42, 44, 1, 600, 25, 52, 27, 812, 1, 2700, 1, 32, 66, 68, 70, 2592, 1, 76, 78, 1640, 1, 5292, 1, 1980, 2070, 92, 1, 2352, 49, 2550, 102, 2756, 1, 2970, 110, 3192, 114, 116, 1, 223200, 1, 124, 4032

Offset

1,4

Links

Table of n, a(n) for n=1..63.

Formula

a(p^k) = 1 for p prime and k = 1, else p^k if k >= 2. - Wesley Ivan Hurt, Jun 26 2024

Mathematica

Table[DivisorSum[n, n^PrimeNu[n/#] &, PrimeQ[#] &], {n, 100}]

Crossrefs

Cf. A001221 (omega), A345354, A345355.

Sequence in context: A225770 A019304 A072869 * A064279 A369908 A078710

Adjacent sequences: A369902 A369903 A369904 * A369906 A369907 A369908

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved