A351517 a(n) = Product_{p|n, p prime} p^(pi(p) mod 2).

1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 11, 2, 1, 2, 5, 2, 17, 2, 1, 10, 1, 22, 23, 2, 5, 2, 1, 2, 1, 10, 31, 2, 11, 34, 5, 2, 1, 2, 1, 10, 41, 2, 1, 22, 5, 46, 47, 2, 1, 10, 17, 2, 1, 2, 55, 2, 1, 2, 59, 10, 1, 62, 1, 2, 5, 22, 67, 34, 23, 10, 1, 2, 73, 2, 5, 2, 11, 2, 1, 10, 1, 82, 83, 2, 85

Offset

1,2

Comments

Product of the odd-indexed prime divisors of n (or 1 if no such divisors exist).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007947(n)/A351518(n). - Amiram Eldar, Nov 15 2025

Example

a(30) = 10; The odd-indexed prime divisors of 30 are 2,5 and their product is 10.

Maple

f:= n ->
 convert(select(t -> numtheory:-pi(t)::odd, numtheory:-factorset(n)), `*`):
map(f, [$1..100]); # Robert Israel, Oct 30 2025

Mathematica

A351517[n_] := Times @@ Select[FactorInteger[n][[All, 1]], OddQ[PrimePi[#]] &];
Array[A351517, 100] (* Paolo Xausa, Oct 31 2025 *)

Prog

(PARI) a(n) = vecprod(apply(p -> if(primepi(p) % 2, p, 1), factor(n)[, 1])); \\ Amiram Eldar, Nov 15 2025

Crossrefs

Cf. A000720 (pi), A007947 (rad), A351518.

Sequence in context: A295516 A330209 A068822 * A337224 A090079 A165195

Adjacent sequences: A351514 A351515 A351516 * A351518 A351519 A351520

Keyword

nonn,mult

Author

Wesley Ivan Hurt, Feb 12 2022

Status

approved