A338490 Sum of indices of distinct odd prime factors of n.

0, 0, 2, 0, 3, 2, 4, 0, 2, 3, 5, 2, 6, 4, 5, 0, 7, 2, 8, 3, 6, 5, 9, 2, 3, 6, 2, 4, 10, 5, 11, 0, 7, 7, 7, 2, 12, 8, 8, 3, 13, 6, 14, 5, 5, 9, 15, 2, 4, 3, 9, 6, 16, 2, 8, 4, 10, 10, 17, 5, 18, 11, 6, 0, 9, 7, 19, 7, 11, 7, 20, 2, 21, 12, 5, 8, 9, 8, 22, 3, 2, 13, 23, 6, 10, 14, 12, 5, 24, 5

Offset: 1

Author

Ilya Gutkovskiy, Nov 09 2020

Keywords

• nonn

Examples

			a(60) = a(2^2 * 3 * 5) = a(prime(1)^2 * prime(2) * prime(3)) = 2 + 3 = 5.
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A000720, A005069, A005087, A056239, A066328.

Programs

Mathematica

nmax = 90; CoefficientList[Series[Sum[k x^Prime[k]/(1 - x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x] // Rest

PARI

a(n) = vecsum(apply(primepi, (factor(n >> valuation(n, 2))[, 1]))); \\ Michel Marcus, Nov 10 2020

Formula

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

a(n) = Sum_{p|n, p odd prime} A000720(p).

a(n) = A066328(A000265(n)).