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.

A370297 Inverse Moebius transform of A322328.

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%I A370297 #9 Feb 16 2024 09:56:43
%S A370297 1,5,5,13,5,25,5,25,13,25,5,65,5,25,25,41,5,65,5,65,25,25,5,125,13,25,
%T A370297 25,65,5,125,5,61,25,25,25,169,5,25,25,125,5,125,5,65,65,25,5,205,13,
%U A370297 65,25,65,5,125,25,125,25,25,5,325,5,25,65,85,25,125,5,65,25,125,5,325
%N A370297 Inverse Moebius transform of A322328.
%F A370297 Multiplicative with a(p^e) = 1 + 2*e*(e+1) for prime p and e >= 0.
%F A370297 Dirichlet g.f.: (zeta(s))^5 / (zeta(2*s))^2.
%F A370297 Dirichlet convolution of A034444 and A048691.
%F A370297 Dirichlet inverse sequence b(n) for n > 0 is multiplicative with b(p) = -5 and b(p^e) = (-1)^e * (8*e-4) for prime p and e > 1.
%t A370297 f[p_, e_] := 2*e^2 + 2*e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 14 2024 *)
%o A370297 (PARI) a(n) = factorback(apply(e->1+2*e*(e+1), factor(n)[,2]))
%Y A370297 Cf. A034444, A048691, A322328.
%K A370297 nonn,easy,mult
%O A370297 1,2
%A A370297 _Werner Schulte_, Feb 14 2024