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A116073
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Sum of the divisors of n that are not divisible by 5.
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16
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1, 3, 4, 7, 1, 12, 8, 15, 13, 3, 12, 28, 14, 24, 4, 31, 18, 39, 20, 7, 32, 36, 24, 60, 1, 42, 40, 56, 30, 12, 32, 63, 48, 54, 8, 91, 38, 60, 56, 15, 42, 96, 44, 84, 13, 72, 48, 124, 57, 3, 72, 98, 54, 120, 12, 120, 80, 90, 60, 28, 62, 96, 104, 127, 14, 144, 68, 126, 96, 24
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OFFSET
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1,2
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).
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LINKS
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FORMULA
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a(n) is multiplicative with a(5^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) otherwise.
G.f.: Sum_{k>0} k*x^k/(1-x^k) - 5*k*x^(5*k)/(1-x^(5*k)).
L.g.f.: log(Product_{k>=1} (1 - x^(5*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 14 2018
Sum_{k=1..n} a(k) ~ (Pi^2/15) * n^2. - Amiram Eldar, Oct 04 2022
Inverse Mobius transf. of A091703. Dirichlet g.f. (1-5^(1-s))*zeta(s-1)*zeta(s). - R. J. Mathar, May 17 2023
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MATHEMATICA
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f[p_, e_] := If[p == 5, 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) = if(n<1, 0, sumdiv(n, d, (d%5>0)*d))
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CROSSREFS
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Cf. A091703, A035207 (number of divisors of n that are not divisible by 5).
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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