A328878 If n = Product (p_j^k_j) then a(n) = Product (prime(p_j)).

1, 3, 5, 3, 11, 15, 17, 3, 5, 33, 31, 15, 41, 51, 55, 3, 59, 15, 67, 33, 85, 93, 83, 15, 11, 123, 5, 51, 109, 165, 127, 3, 155, 177, 187, 15, 157, 201, 205, 33, 179, 255, 191, 93, 55, 249, 211, 15, 17, 33, 295, 123, 241, 15, 341, 51, 335, 327, 277, 165, 283, 381, 85, 3, 451

Offset: 1

Author

Ilya Gutkovskiy, Oct 29 2019

Keywords

• nonn
• mult

Examples

			a(54) = 15 because 54 = 2 * 3^3 = prime(1) * prime(2)^3 and prime(prime(1)) * prime(prime(2)) = 3 * 5 = 15.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A006450, A007947, A064988, A156061, A181819, A321874.

Programs

Maple

a:= n-> mul(ithprime(i[1]), i=ifactors(n)[2]):
seq(a(n), n=1..65);  # Alois P. Heinz, Nov 26 2024

Mathematica

a[n_] := Times @@ (Prime[#[[1]]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 65}]

PARI

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