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A284587
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Sum of the divisors of n that are not divisible by 13.
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4
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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
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OFFSET
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1,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..10000
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=sumdiv(n, d, ((d%13)>0)*d); \\ Andrew Howroyd, Jul 20 2018
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CROSSREFS
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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).
Sequence in context: A069192 A076887 A140782 * A097011 A074847 A325317
Adjacent sequences: A284584 A284585 A284586 * A284588 A284589 A284590
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KEYWORD
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nonn,mult
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AUTHOR
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Seiichi Manyama, Mar 29 2017
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EXTENSIONS
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Keyword:mult added by Andrew Howroyd, Jul 20 2018
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STATUS
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approved
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