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 A343442 #19 Jul 25 2025 14:30:10
%S A343442 1,4,5,4,7,20,9,4,5,28,13,20,15,36,35,4,19,20,21,28,45,52,25,20,7,60,
%T A343442 5,36,31,140,33,4,65,76,63,20,39,84,75,28,43,180,45,52,35,100,49,20,9,
%U A343442 28,95,60,55,20,91,36,105,124,61,140,63,132,45,4,105,260,69,76,125,252
%N A343442 If n = Product (p_j^k_j) then a(n) = Product (p_j + 2), with a(1) = 1.
%H A343442 Amiram Eldar, <a href="/A343442/b343442.txt">Table of n, a(n) for n = 1..10000</a>
%H A343442 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%F A343442 G.f.: Sum_{k>=1} mu(k)^2 * sigma(k) * x^k / (1 - x^k), where mu = A008683 and sigma = A000203.
%F A343442 a(n) = Sum_{d|n} mu(d)^2 * sigma(d).
%F A343442 Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/(12*zeta(3)) = 0.684216... (A335005). - _Amiram Eldar_, Nov 13 2022
%F A343442 a(n) = Sum_{d|n} mu(d)^2*psi(d), where psi is A001615. - _Ridouane Oudra_, Jul 24 2025
%t A343442 a[1] = 1; a[n_] := Times @@ ((#[[1]] + 2) & /@ FactorInteger[n]); Table[a[n], {n, 70}]
%t A343442 nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k]^2 DivisorSigma[1, k] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A343442 (PARI) a(n) = sumdiv(n, d, moebius(d)^2 * sigma(d)) \\ _Andrew Howroyd_, Apr 15 2021
%Y A343442 Cf. A000203, A001615, A007429, A007947, A008683, A048250, A062953, A063441, A074816, A092261, A107758, A107759, A319132, A335005.
%K A343442 nonn,mult
%O A343442 1,2
%A A343442 _Ilya Gutkovskiy_, Apr 15 2021