This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116073 #27 May 17 2023 04:21:11 %S A116073 1,3,4,7,1,12,8,15,13,3,12,28,14,24,4,31,18,39,20,7,32,36,24,60,1,42, %T A116073 40,56,30,12,32,63,48,54,8,91,38,60,56,15,42,96,44,84,13,72,48,124,57, %U A116073 3,72,98,54,120,12,120,80,90,60,28,62,96,104,127,14,144,68,126,96,24 %N A116073 Sum of the divisors of n that are not divisible by 5. %D A116073 B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 463 Entry 4(i). %H A116073 Seiichi Manyama, <a href="/A116073/b116073.txt">Table of n, a(n) for n = 1..10000</a> %F A116073 a(n) is multiplicative with a(5^e) = 1, a(p^e) = (p^(e+1)-1)/(p-1) otherwise. %F A116073 G.f.: Sum_{k>0} k*x^k/(1-x^k) - 5*k*x^(5*k)/(1-x^(5*k)). %F A116073 L.g.f.: log(Product_{k>=1} (1 - x^(5*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, Mar 14 2018 %F A116073 Sum_{k=1..n} a(k) ~ (Pi^2/15) * n^2. - _Amiram Eldar_, Oct 04 2022 %F A116073 Inverse Mobius transf. of A091703. Dirichlet g.f. (1-5^(1-s))*zeta(s-1)*zeta(s). - _R. J. Mathar_, May 17 2023 %t A116073 f[p_, e_] := If[p == 5, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 17 2020 *) %o A116073 (PARI) a(n) = if(n<1, 0, sumdiv(n,d,(d%5>0)*d)) %Y A116073 Cf. A028887(n) = 6*a(n) if n>0. %Y A116073 Cf. A145466. %Y A116073 Cf. A091703, A035207 (number of divisors of n that are not divisible by 5). %K A116073 nonn,mult %O A116073 1,2 %A A116073 _Michael Somos_, Feb 04 2006