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 A360997 #14 Sep 01 2023 04:09:05
%S A360997 1,4,4,5,4,16,4,6,5,16,4,20,4,16,16,7,4,20,4,20,16,16,4,24,5,16,6,20,
%T A360997 4,64,4,8,16,16,16,25,4,16,16,24,4,64,4,20,20,16,4,28,5,20,16,20,4,24,
%U A360997 16,24,16,16,4,80,4,16,20,9,16,64,4,20,16,64,4,30,4,16
%N A360997 Multiplicative with a(p^e) = e + 3.
%H A360997 Amiram Eldar, <a href="/A360997/b360997.txt">Table of n, a(n) for n = 1..10000</a>
%F A360997 Dirichlet g.f.: Product_{primes p} (1 + (4*p^s - 3)/(p^s - 1)^2).
%F A360997 Dirichlet g.f.: zeta(s)^4 * Product_{primes p} (1 - 5/p^(2*s) + 6/p^(3*s) - 2/p^(4*s)).
%F A360997 From _Amiram Eldar_, Sep 01 2023: (Start)
%F A360997 a(n) = A000005(A361264(n)).
%F A360997 a(n) = A074816(n)*A007426(n)/A007425(n). (End)
%t A360997 g[p_, e_] := e+3; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]
%o A360997 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1+2*X-2*X^2)/(1-X)^2)[n], ", "))
%Y A360997 Cf. A005361 (multiplicative with a(p^e) = e), A000005 (e+1), A343443 (e+2), this sequence (e+3), A322327 (2*e), A048691 (2*e+1), A360908 (2*e-1), A226602 (3*e), A048785 (3*e+1), A360910 (3*e-1), A360909 (3*e+2), A360911 (3*e-2), A322328 (4*e), A360996 (5*e).
%Y A360997 Cf. A000005, A007425, A007426, A074816.
%K A360997 nonn,easy,mult
%O A360997 1,2
%A A360997 _Vaclav Kotesovec_, Feb 28 2023