A345354 a(n) = Sum_{p|n, p prime} omega(n/p).

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 1, 0, 3, 0, 3, 2, 2, 0, 3, 1, 2, 1, 3, 0, 6, 0, 1, 2, 2, 2, 4, 0, 2, 2, 3, 0, 6, 0, 3, 3, 2, 0, 3, 1, 3, 2, 3, 0, 3, 2, 3, 2, 2, 0, 7, 0, 2, 3, 1, 2, 6, 0, 3, 2, 6, 0, 4, 0, 2, 3, 3, 2, 6, 0, 3, 1, 2, 0, 7, 2, 2, 2, 3, 0, 7, 2, 3

Offset: 1

Author

Wesley Ivan Hurt, Jun 15 2021

Keywords

• nonn

Examples

			a(30) = Sum_{p|30} omega(30/p) = omega(15) + omega(10) + omega(6) = 2 + 2 + 2 = 6.
		

Crossrefs

Cf. A001221 (omega).

Programs

Mathematica

Table[Sum[PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, omega(n/f[k,1])); \\ Michel Marcus, Jun 16 2021

Formula

a(p) = 0 for p prime.

a(n) = Sum_{a*b*c=n} omega(a)*omega(b)*mu(c). - Benedict W. J. Irwin, Mar 02 2022