A284587 Sum of the divisors of n that are not divisible by 13.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 1, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 3, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 4, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 7, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 6, 144, 68

Offset: 1

Author

Seiichi Manyama, Mar 29 2017

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A000203, A133099.

Sum of the divisors of n that are not divisible by k: A046913 (k=3), A046897 (k=4), A116073 (k=5), A284326 (k=6), A113957 (k=7), A284341 (k=8), A116607 (k=9), A284344 (k=10), this sequence (k=13), A227131 (k=25).

Programs

Mathematica

Table[Sum[Boole[Mod[d, 13]>0] d , {d, Divisors[n]}], {n, 100}] (* Indranil Ghosh, Mar 29 2017 *)
f[p_, e_] := If[p == 13, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *)

PARI

a(n)=sumdiv(n, d, ((d%13)>0)*d); \\ Andrew Howroyd, Jul 20 2018

Formula

G.f.: Sum_{k>=1} k*x^k/(1 - x^k) - 13*k*x^(13*k)/(1 - x^(13*k)). - Ilya Gutkovskiy, Mar 30 2017

Multiplicative with a(13^e) = 1 and a(p^e) = (p^(e+1)-1)/(p-1) otherwise. - Amiram Eldar, Sep 17 2020

Sum_{k=1..n} a(k) ~ (Pi^2/13) * n^2. - Amiram Eldar, Oct 04 2022

Extensions

Keyword:mult added by Andrew Howroyd, Jul 20 2018