A113957 Sum of the divisors of n which are not divisible by 7.

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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A113954 A113955 A113956 * A113958 A113959 A113960

Keyword

nonn,mult

Author

Michael Somos, Nov 10 2005

Status

approved