A284326 Sum of the divisors of n that are not divisible by 6.

1, 3, 4, 7, 6, 6, 8, 15, 13, 18, 12, 10, 14, 24, 24, 31, 18, 15, 20, 42, 32, 36, 24, 18, 31, 42, 40, 56, 30, 36, 32, 63, 48, 54, 48, 19, 38, 60, 56, 90, 42, 48, 44, 84, 78, 72, 48, 34, 57, 93, 72, 98, 54, 42, 72, 120, 80, 90, 60, 60, 62, 96, 104, 127, 84, 72, 68

Offset: 1

Author

Seiichi Manyama, Mar 25 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. Sum of the divisors of n that are not divisible by k: A046913 (k=3), A046897 (k=4), A116073 (k=5), this sequence (k=6), A113957 (k=7), A284341 (k=8), A116607 (k=9), A284344 (k=10).

Programs

Mathematica

Table[Sum[Boole[Mod[d,6]>0] d , {d, Divisors[n]}], {n,100}] (* Indranil Ghosh, Mar 25 2017 *)
Table[Total[Select[Divisors[n],Mod[#,6]!=0&]],{n,100}] (* Harvey P. Dale, Feb 25 2020 *)

PARI

for(n=1, 100, print1(sumdiv(n, d, ((d%6)>0)*d),", ")) \\ Indranil Ghosh, Mar 25 2017

Python

from sympy import divisors
print([sum([i for i in divisors(n) if i%6]) for n in range(1, 101)]) # Indranil Ghosh, Mar 25 2017

Formula

G.f.: Sum_{k>=1} k*x^k/(1 - x^k) - 6*k*x^(6*k)/(1 - x^(6*k)). - Ilya Gutkovskiy, Mar 25 2017

Sum_{k=1..n} a(k) ~ (5*Pi^2/72) * n^2. - Amiram Eldar, Oct 04 2022

Dirichlet g.f. (1-6^(1-s))*zeta(s-1)*zeta(s), but not multiplicative. - R. J. Mathar, May 17 2023