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%I #41 Oct 04 2022 12:36:02
%S 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,
%T 3,40,56,30,72,32,63,48,54,48,91,38,60,4,90,42,96,44,84,78,72,48,124,
%U 57,93,72,7,54,120,72,120,80,90,60,168,62,96,104,127,6,144,68
%N Sum of the divisors of n that are not divisible by 13.
%H Seiichi Manyama, <a href="/A284587/b284587.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%F Multiplicative with a(13^e) = 1 and a(p^e) = (p^(e+1)-1)/(p-1) otherwise. - _Amiram Eldar_, Sep 17 2020
%F Sum_{k=1..n} a(k) ~ (Pi^2/13) * n^2. - _Amiram Eldar_, Oct 04 2022
%t Table[Sum[Boole[Mod[d, 13]>0] d , {d, Divisors[n]}], {n, 100}] (* _Indranil Ghosh_, Mar 29 2017 *)
%t 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 *)
%o (PARI) a(n)=sumdiv(n, d, ((d%13)>0)*d); \\ _Andrew Howroyd_, Jul 20 2018
%Y Cf. A000203, A133099.
%Y 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).
%K nonn,mult
%O 1,2
%A _Seiichi Manyama_, Mar 29 2017
%E Keyword:mult added by _Andrew Howroyd_, Jul 20 2018
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