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A338490 Sum of indices of distinct odd prime factors of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A077961 A077962 A338101 * A213607 A298932 A089196

Adjacent sequences:  A338487 A338488 A338489 * A338491 A338492 A338493

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 09 2020

STATUS

approved

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Last modified June 23 02:02 EDT 2021. Contains 345395 sequences. (Running on oeis4.)