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A116073 Sum of the divisors of n that are not divisible by 5. 15

%I

%S 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,

%T 40,56,30,12,32,63,48,54,8,91,38,60,56,15,42,96,44,84,13,72,48,124,57,

%U 3,72,98,54,120,12,120,80,90,60,28,62,96,104,127,14,144,68,126,96,24

%N Sum of the divisors of n that are not divisible by 5.

%D B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i).

%H Seiichi Manyama, <a href="/A116073/b116073.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) is multiplicative with a(5^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) otherwise.

%F G.f.: Sum_{k>0} k*x^k/(1-x^k) - 5*k*x^(5*k)/(1-x^(5*k)).

%F 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

%t 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 *)

%o (PARI) a(n) = if(n<1, 0, sumdiv(n,d,(d%5>0)*d))

%Y Cf. A028887(n) = 6*a(n) if n>0.

%Y Cf. A145466.

%Y Cf. A035207 (number of divisors of n that are not divisible by 5).

%K nonn,mult

%O 1,2

%A _Michael Somos_, Feb 04 2006

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Last modified April 17 15:33 EDT 2021. Contains 343063 sequences. (Running on oeis4.)