A328915 If n = Product (p_j^k_j) then a(n) = Product (nextprime(p_j)), where nextprime = A151800.

1, 3, 5, 3, 7, 15, 11, 3, 5, 21, 13, 15, 17, 33, 35, 3, 19, 15, 23, 21, 55, 39, 29, 15, 7, 51, 5, 33, 31, 105, 37, 3, 65, 57, 77, 15, 41, 69, 85, 21, 43, 165, 47, 39, 35, 87, 53, 15, 11, 21, 95, 51, 59, 15, 91, 33, 115, 93, 61, 105, 67, 111, 55, 3, 119, 195, 71, 57, 145, 231

Offset: 1

Author

Ilya Gutkovskiy, Oct 30 2019

Keywords

• nonn
• mult

Comments

All terms are odd.

Examples

			a(12) = a(2^2 * 3) = a(prime(1)^2 * prime(2)) = prime(2) * prime(3) = 3 * 5 = 15.
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000720, A003961, A007947, A045965, A045967, A048250, A151800, A328878, A328879.

Programs

Maple

a:= n-> mul(nextprime(i[1]), i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 30 2019

Mathematica

a[1] = 1; a[n_] := Times @@ (NextPrime[#[[1]]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 70}]

PARI

a(n) = my(f=factor(n)); prod(k=1, #f~, nextprime(f[k,1]+1)); \\ Michel Marcus, Oct 30 2019

Formula

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

a(n) = A007947(A003961(n)).