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A285896
Sum of divisors d of n such that n/d is not congruent to 0 mod 5.
5
1, 3, 4, 7, 5, 12, 8, 15, 13, 15, 12, 28, 14, 24, 20, 31, 18, 39, 20, 35, 32, 36, 24, 60, 25, 42, 40, 56, 30, 60, 32, 63, 48, 54, 40, 91, 38, 60, 56, 75, 42, 96, 44, 84, 65, 72, 48, 124, 57, 75, 72, 98, 54, 120, 60, 120, 80, 90, 60, 140, 62, 96, 104, 127, 70, 144
OFFSET
1,2
LINKS
FORMULA
a(n) = (A000203(5*n)-A000203(n))/5.
G.f.: Sum_{k>=1} k*x^k*(1 + x^k + x^(2*k) + x^(3*k))/(1 - x^(5*k)). - Ilya Gutkovskiy, Sep 12 2019
From Amiram Eldar, Oct 30 2022: (Start)
Multiplicative with a(5^e) = 5^e and a(p^e) = (p^(e+1)-1)/(p-1) if p != 5.
Sum_{k=1..n} a(k) ~ c * n^2, where c = 2*Pi^2/25 = 0.789568... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-1)*(1-1/5^s). - Amiram Eldar, Dec 30 2022
EXAMPLE
The divisors of 10 are 1, 2, 5, and 10. 10/1 == 0 (mod 5) and 10/2 == 0 (mod 5). Hence, a(10) = 5 + 10 = 15.
MATHEMATICA
f[p_, e_] := If[p == 5, 5^e, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 30 2022 *)
PROG
(PARI) a(n)=sumdiv(n, d, if(n/d%5, d, 0)); \\ Andrew Howroyd, Jul 20 2018
CROSSREFS
Cf. A002131 (k=2), A078708 (k=3), A285895 (k=4), this sequence (k=5).
Cf. A000203.
Sequence in context: A338285 A050197 A003975 * A082226 A010613 A299693
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Apr 28 2017
EXTENSIONS
Keyword:mult added by Andrew Howroyd, Jul 20 2018
STATUS
approved