A370328 - OEIS

%I #8 Feb 16 2024 02:10:54

%S 1,2,3,2,4,2,3,5,4,2,6,6,4,4,6,2,3,7,8,2,4,6,9,4,5,8,10,2,8,3,2,6,8,

%T 12,4,4,6,9,2,12,4,12,6,4,6,8,10,2,15,8,2,6,10,9,10,4,6,14,4,4,16,6,3,

%U 6,2,6,4,4,10,12,2,18,8,12,2,8,15,12,8,11,4,7

%N The number of powerful divisors of the powerful numbers.

%C The product of the exponents of the prime factorization of the powerful numbers.

%H Amiram Eldar, <a href="/A370328/b370328.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A005361(A001694(n)).

%F a(n) = A000005(A306458(n)).

%t f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[n == 1 || Min[e] > 1, Times @@ e, Nothing]]; Array[f, 2500]

%o (PARI) lista(kmax) = {my(e); for(k = 1, kmax, e = factor(k)[,2]; if(k == 1 || vecmin(e) > 1, print1(vecprod(e), ", ")));}

%Y Cf. A000005, A001694, A005361, A306458, A363194, A370329.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Feb 15 2024