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) - 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
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 *)
PROG
(PARI) a(n)=sumdiv(n, d, ((d%13)>0)*d); \\ Andrew Howroyd, Jul 20 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Mar 29 2017
EXTENSIONS
Keyword:mult added by Andrew Howroyd, Jul 20 2018
STATUS
approved