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

1,2

Links

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

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

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 *)

Prog

(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

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).

Sequence in context: A023888 A222085 A187793 * A117553 A331694 A290270

Adjacent sequences: A284323 A284324 A284325 * A284327 A284328 A284329

Keyword

nonn

Author

Seiichi Manyama, Mar 25 2017

Status

approved