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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 (list; graph; refs; listen; history; text; internal format)
 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 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: A057032 A279388 A292288 * A073185 A284341 A073183 Adjacent sequences:  A113954 A113955 A113956 * A113958 A113959 A113960 KEYWORD nonn,mult AUTHOR Michael Somos, Nov 10 2005 STATUS approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)