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%I #10 Oct 29 2019 12:15:38
%S 1,2,3,2,4,6,3,2,3,8,5,6,7,6,12,2,4,6,3,8,9,10,4,6,4,14,3,6,9,24,6,2,
%T 15,8,12,6,7,6,21,8,8,18,7,10,12,8,13,6,3,8,12,14,3,6,20,6,9,18,5,24,
%U 7,12,9,2,28,30,4,8,12,24,9,6,10,14,12,6,15,42,11,8
%N If n = Product (p_j^k_j) then a(n) = Product (a(pi(p_j)) + 1), where pi = A000720, with a(1) = 1.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = a(prime(n)) - 1.
%e a(36) = 6 because 36 = 2^2 * 3^2 = prime(1)^2 * prime(2)^2 and (a(1) + 1) * (a(2) + 1) = (1 + 1) * (2 + 1) = 6.
%t a[1] = 1; a[n_] := Times @@ (a[PrimePi[#[[1]]]] + 1 & /@ FactorInteger[n]); Table[a[n], {n, 1, 80}]
%o (PARI) a(n)={my(f=factor(n)[,1]); prod(i=1, #f, 1 + a(primepi(f[i])))} \\ _Andrew Howroyd_, Oct 29 2019
%Y Cf. A000720, A048250, A156061, A184160, A225395, A282446, A328879.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Oct 29 2019
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