cp's OEIS Frontend

A318519 a(n) = A000005(n) * A003557(n).

%I A318519 #14 Sep 14 2023 02:31:25
%S A318519 1,2,2,6,2,4,2,16,9,4,2,12,2,4,4,40,2,18,2,12,4,4,2,32,15,4,36,12,2,8,
%T A318519 2,96,4,4,4,54,2,4,4,32,2,8,2,12,18,4,2,80,21,30,4,12,2,72,4,32,4,4,2,
%U A318519 24,2,4,18,224,4,8,2,12,4,8,2,144,2,4,30,12,4,8,2,80,135,4,2,24,4,4,4,32,2,36,4,12,4,4,4,192,2,42,18,90,2,8,2,32,8
%N A318519 a(n) = A000005(n) * A003557(n).
%H A318519 Antti Karttunen, <a href="/A318519/b318519.txt">Table of n, a(n) for n = 1..65537</a>
%F A318519 Multiplicative with a(p^e) = (e+1)*(p^(e-1)).
%F A318519 a(n) = A000005(n) * A003557(n).
%F A318519 a(n) = A062355(n) / A173557(n).
%F A318519 Dirichlet g.f.: zeta(s-1)^2 * Product_{p prime} (1 - 2/p^(s-1) + 2/p^s - 1/p^(2*s-1) + 1/p^(2*s-2)). - _Amiram Eldar_, Sep 14 2023
%t A318519 f[p_, e_] := (e + 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 14 2023 *)
%o A318519 (PARI)
%o A318519 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A318519 A318519(n) = (numdiv(n)*A003557(n));
%o A318519 (PARI) A318519(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i,2]+1)*(f[i,1]^(f[i,2]-1))); };
%Y A318519 Cf. A000005, A003557, A062355, A173557.
%K A318519 nonn,easy,mult
%O A318519 1,2
%A A318519 _Antti Karttunen_, Sep 16 2018