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A328879
If n = Product (p_j^k_j) then a(n) = Product (pi(p_j) + 1), where pi = A000720.
2
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, 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, 10, 27, 22, 18, 24, 19, 24, 15, 2, 28, 36, 20, 16, 30, 40, 21, 6, 22, 26, 12
OFFSET
1,2
COMMENTS
a(n) is the product of indices of distinct prime factors of n if 1 is considered as a prime (see A008578).
EXAMPLE
a(36) = 6 because 36 = 2^2 * 3^2 = prime(1)^2 * prime(2)^2 and (1 + 1) * (2 + 1) = 6.
MATHEMATICA
a[n_] := Times @@ ((PrimePi[#[[1]]] + 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 75}]
PROG
(PARI) a(n)={my(f=factor(n)[, 1]); prod(i=1, #f, 1 + primepi(f[i]))} \\ Andrew Howroyd, Oct 29 2019
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Oct 29 2019
STATUS
approved