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

1,3

Links

Table of n, a(n) for n=1..90.

Index entries for sequences computed from indices in prime factorization

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)).

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A353484 A349134 A338101 * A213607 A298932 A089196

Adjacent sequences: A338487 A338488 A338489 * A338491 A338492 A338493

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 09 2020

Status

approved