A279051 Sum of odd nonprime divisors of n.

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

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: A360160 A360159 A284100 * A332804 A010178 A070596

Adjacent sequences: A279048 A279049 A279050 * A279052 A279053 A279054

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 17 2017

Status

approved