cp's OEIS Frontend

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.

A325211 a(1) = 1; a(n) = Sum_{d|n, d tau(n/d) * a(d), where tau = A000005.

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%I A325211 #17 Sep 05 2019 15:47:36
%S A325211 1,2,2,7,2,12,2,24,7,12,2,58,2,12,12,82,2,58,2,58,12,12,2,256,7,12,24,
%T A325211 58,2,104,2,280,12,12,12,355,2,12,12,256,2,104,2,58,58,12,2,1072,7,58,
%U A325211 12,58,2,256,12,256,12,12,2,652,2,12,58,956,12,104,2,58,12,104
%N A325211 a(1) = 1; a(n) = Sum_{d|n, d<n} tau(n/d) * a(d), where tau = A000005.
%F A325211 G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} tau(k) * A(x^k).
%F A325211 a(p) = 2, where p is prime.
%t A325211 a[n_] := If[n == 1, n, Sum[If[d < n, DivisorSigma[0, n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 70}]
%t A325211 nmax = 70; A[_] = 0; Do[A[x_] = x + Sum[DivisorSigma[0, k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%o A325211 (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n] = sumdiv(n, d, v[d]*numdiv(n/d))); v} \\ _Andrew Howroyd_, Sep 05 2019
%Y A325211 Cf. A000005, A007427, A007557, A325212.
%K A325211 nonn
%O A325211 1,2
%A A325211 _Ilya Gutkovskiy_, Sep 05 2019