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A113957
Sum of the divisors of n which are not divisible by 7.
13
1, 3, 4, 7, 6, 12, 1, 15, 13, 18, 12, 28, 14, 3, 24, 31, 18, 39, 20, 42, 4, 36, 24, 60, 31, 42, 40, 7, 30, 72, 32, 63, 48, 54, 6, 91, 38, 60, 56, 90, 42, 12, 44, 84, 78, 72, 48, 124, 1, 93, 72, 98, 54, 120, 72, 15, 80, 90, 60, 168, 62, 96, 13, 127, 84, 144, 68, 126, 96, 18, 72
OFFSET
1,2
REFERENCES
B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 467, Entry 5(i).
LINKS
FORMULA
a(n) is multiplicative and a(p^e) = 1, if p=7, a(p^e) = (p^(e+1)-1)/(p-1) otherwise.
G.f.: ((theta_3(z)*theta_3(7z) + theta_2(z)*theta_2(7z))^2-1)/4.
L.g.f.: log(Product_{k>=1} (1 - x^(7*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 14 2018
Sum_{k=1..n} a(k) ~ (Pi^2/14) * n^2. - Amiram Eldar, Oct 04 2022
Dirichlet g.f. (1-7^(1-s))*zeta(s)*zeta(s-1). - R. J. Mathar, May 17 2023
MATHEMATICA
f[p_, e_] := If[p == 7, 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, sigma(n/7^valuation(n, 7)))
CROSSREFS
Cf. A028594(n)=4*a(n) if n>0.
Cf. A244600.
Sequence in context: A292288 A347273 A355584 * A366148 A367171 A348946
KEYWORD
nonn,mult
AUTHOR
Michael Somos, Nov 10 2005
STATUS
approved