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A116073
Sum of the divisors of n that are not divisible by 5.
16
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
OFFSET
1,2
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).
LINKS
FORMULA
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
MATHEMATICA
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 *)
PROG
(PARI) a(n) = if(n<1, 0, sumdiv(n, d, (d%5>0)*d))
CROSSREFS
Cf. A028887(n) = 6*a(n) if n>0.
Cf. A145466.
Cf. A091703, A035207 (number of divisors of n that are not divisible by 5).
Sequence in context: A376212 A130893 A072079 * A166043 A294896 A021292
KEYWORD
nonn,mult
AUTHOR
Michael Somos, Feb 04 2006
STATUS
approved