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 A370296 #13 Feb 15 2024 13:02:13 %S A370296 1,3,3,7,3,9,3,13,7,9,3,21,3,9,9,21,3,21,3,21,9,9,3,39,7,9,13,21,3,27, %T A370296 3,31,9,9,9,49,3,9,9,39,3,27,3,21,21,9,3,63,7,21,9,21,3,39,9,39,9,9,3, %U A370296 63,3,9,21,43,9,27,3,21,9,27,3,91,3,9,21,21,9,27,3,63,21,9,3,63 %N A370296 Inverse Moebius transform of A322327. %F A370296 Multiplicative with a(p^e) = 1 + e + e^2 for prime p and e >= 0. %F A370296 Dirichlet g.f.: (zeta(s))^3 * zeta(2*s) / zeta(4*s). %F A370296 Dirichlet inverse sequence b(n) for n > 0 is multiplicative with b(p) = -3 and b(p^e) = 2 * (-1)^((e+1)*(e+2)/2) for prime p and e > 1. %F A370296 Dirichlet convolution of A000005 and A323308. %t A370296 f[p_, e_] := e^2 + e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 14 2024 *) %o A370296 (PARI) a(n) = factorback(apply(e->1+e+e^2,factor(n)[,2])) %Y A370296 Cf. A322327, A000005, A323308. %K A370296 nonn,easy,mult %O A370296 1,2 %A A370296 _Werner Schulte_, Feb 14 2024