

A328880


If n = Product (p_j^k_j) then a(n) = Product (a(pi(p_j)) + 1), where pi = A000720, with a(1) = 1.


3



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, 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, 7, 12, 9, 2, 28, 30, 4, 8, 12, 24, 9, 6, 10, 14, 12, 6, 15, 42, 11, 8
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..80.
Index entries for sequences computed from indices in prime factorization


FORMULA

a(n) = a(prime(n))  1.


EXAMPLE

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.


MATHEMATICA

a[1] = 1; a[n_] := Times @@ (a[PrimePi[#[[1]]]] + 1 & /@ FactorInteger[n]); Table[a[n], {n, 1, 80}]


PROG

(PARI) a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + a(primepi(f[i])))} \\ Andrew Howroyd, Oct 29 2019


CROSSREFS

Cf. A000720, A048250, A156061, A184160, A225395, A282446, A328879.
Sequence in context: A215190 A214943 A202864 * A291290 A006047 A285712
Adjacent sequences: A328877 A328878 A328879 * A328881 A328882 A328883


KEYWORD

nonn,mult


AUTHOR

Ilya Gutkovskiy, Oct 29 2019


STATUS

approved



