A360996 - OEIS

%I #9 Feb 28 2023 06:01:13

%S 1,5,5,10,5,25,5,15,10,25,5,50,5,25,25,20,5,50,5,50,25,25,5,75,10,25,

%T 15,50,5,125,5,25,25,25,25,100,5,25,25,75,5,125,5,50,50,25,5,100,10,

%U 50,25,50,5,75,25,75,25,25,5,250,5,25,50,30,25,125,5,50,25,125,5,150

%N Multiplicative with a(p^e) = 5*e, p prime and e > 0.

%F Dirichlet g.f.: Product_{primes p} (1 + 5*p^s/(p^s - 1)^2).

%F a(n) = A005361(n) * A082476(n).

%t g[p_, e_] := 5*e; a[1] = 1; a[n_] := Times @@ g @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1+3*X+X^2)/(1-X)^2)[n], ", "))

%Y Cf. A005361 (multiplicative with a(p^e) = e), A000005 (e+1), A343443 (e+2), A360997 (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).

%Y Cf. A082476.

%K nonn,mult

%O 1,2

%A _Vaclav Kotesovec_, Feb 28 2023