A328879 If n = Product (p_j^k_j) then a(n) = Product (pi(p_j) + 1), where pi = A000720.

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).

Links

Table of n, a(n) for n=1..75.

Index entries for sequences computed from indices in prime factorization

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

Crossrefs

Cf. A000720, A007947, A008578, A036234, A048250, A064553, A156061.

Sequence in context: A285712 A062068 A328219 * A130542 A128502 A349382

Adjacent sequences: A328876 A328877 A328878 * A328880 A328881 A328882

Keyword

nonn,mult

Author

Ilya Gutkovskiy, Oct 29 2019

Status

approved