%I #6 Oct 29 2019 12:15:31
%S 1,2,3,2,4,6,5,2,3,8,6,6,7,10,12,2,8,6,9,8,15,12,10,6,4,14,3,10,11,24,
%T 12,2,18,16,20,6,13,18,21,8,14,30,15,12,12,20,16,6,5,8,24,14,17,6,24,
%U 10,27,22,18,24,19,24,15,2,28,36,20,16,30,40,21,6,22,26,12
%N If n = Product (p_j^k_j) then a(n) = Product (pi(p_j) + 1), where pi = A000720.
%C a(n) is the product of indices of distinct prime factors of n if 1 is considered as a prime (see A008578).
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e a(36) = 6 because 36 = 2^2 * 3^2 = prime(1)^2 * prime(2)^2 and (1 + 1) * (2 + 1) = 6.
%t a[n_] := Times @@ ((PrimePi[#[[1]]] + 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 75}]
%o (PARI) a(n)={my(f=factor(n)[,1]); prod(i=1, #f, 1 + primepi(f[i]))} \\ _Andrew Howroyd_, Oct 29 2019
%Y Cf. A000720, A007947, A008578, A036234, A048250, A064553, A156061.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Oct 29 2019