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A279051 Sum of odd nonprime divisors of n. 1
1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 16, 1, 1, 10, 1, 1, 22, 1, 1, 1, 26, 1, 37, 1, 1, 16, 1, 1, 34, 1, 36, 10, 1, 1, 40, 1, 1, 22, 1, 1, 70, 1, 1, 1, 50, 26, 52, 1, 1, 37, 56, 1, 58, 1, 1, 16, 1, 1, 94, 1, 66, 34, 1, 1, 70, 36, 1, 10, 1, 1, 116, 1, 78, 40, 1, 1, 118, 1, 1, 22, 86, 1, 88, 1, 1, 70, 92, 1, 94, 1, 96, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Odd Divisor Function

Index entries for sequences related to sums of divisors

FORMULA

G.f.: A(x) = B(x) - C(x), where B(x) = Sum_{k>=1} k*x^k/(1 + x^k), C(x) = Sum_{k>=2} prime(k)*x^prime(k)/(1 - x^prime(k)).

a(n) = Sum_{d|n, d odd nonprime} d.

a(A093641(n)) = 1.

EXAMPLE

a(9) = 10 because 9 has 3 divisors {1, 3, 9} among which 2 are odd nonprime {1, 9} therefore 1 + 9 = 10.

MAPLE

with(numtheory):

a:= n-> add(`if`(d::even or d::prime, 0, d), d=divisors(n)):

seq(a(n), n=1..100);  # Alois P. Heinz, Jan 18 2017

MATHEMATICA

Table[DivisorSum[n, #1 &, Mod[#1, 2] == 1 && ! PrimeQ[#1] &], {n, 97}]

nmax = 97; Rest[CoefficientList[Series[Sum[k x^k/(1 + x^k), {k, 1, nmax}] - Sum[Prime[k] x^Prime[k]/(1 - x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]]

PROG

(PARI) a(n) = sumdiv(n, d, !isprime(d)*(d%2)*d); \\ Michel Marcus, Sep 18 2017

CROSSREFS

Cf. A000593, A014076, A023890, A005069, A033272, A093641.

Sequence in context: A307978 A118762 A284100 * A010178 A070596 A306363

Adjacent sequences:  A279048 A279049 A279050 * A279052 A279053 A279054

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 17 2017

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)