A369744 a(n) = Sum_{p|n, p prime} p * omega(n/p).

0, 0, 0, 2, 0, 5, 0, 2, 3, 7, 0, 7, 0, 9, 8, 2, 0, 8, 0, 9, 10, 13, 0, 7, 5, 15, 3, 11, 0, 20, 0, 2, 14, 19, 12, 10, 0, 21, 16, 9, 0, 24, 0, 15, 11, 25, 0, 7, 7, 12, 20, 17, 0, 8, 16, 11, 22, 31, 0, 22, 0, 33, 13, 2, 18, 32, 0, 21, 26, 28, 0, 10, 0, 39, 13, 23, 18, 36

Offset

1,4

Links

Table of n, a(n) for n=1..78.

Formula

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

Mathematica

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

Crossrefs

Cf. A001221 (omega), A323599, A345354, A345355.

Sequence in context: A215339 A061376 A058974 * A326059 A019962 A086131

Adjacent sequences: A369741 A369742 A369743 * A369745 A369746 A369747

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 30 2024

Status

approved