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
KEYWORD
nonn,mult
AUTHOR
Michael Somos, Nov 10 2005
STATUS
approved