A363521 Product of the divisors d of n such that sqrt(n) < d < n.

1, 1, 1, 1, 1, 3, 1, 4, 1, 5, 1, 24, 1, 7, 5, 8, 1, 54, 1, 50, 7, 11, 1, 576, 1, 13, 9, 98, 1, 900, 1, 128, 11, 17, 7, 1944, 1, 19, 13, 1600, 1, 2058, 1, 242, 135, 23, 1, 36864, 1, 250, 17, 338, 1, 4374, 11, 3136, 19, 29, 1, 1080000, 1, 31, 189, 512, 13, 7986, 1, 578, 23

Offset

1,6

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = Product_{d|n, sqrt(n) < d < n} d.

a(n) = A007956(n)/A072499(n).

a(n) = A007955(n)/(n*A072499(n)).

Example

The divisors of 16 are {1,2,4,8,16} and the product of the divisors d of n such that sqrt(16) = 4 < d < 16 is 8, so a(16) = 8.
The divisors of 30 are {1,2,3,5,6,10,15,30} and the product of the divisors d of n such that sqrt(30) < d < 30 is 6*10*15 = 900, so a(30) = 900.

Mathematica

a[n_] := Product[If[n < d^2 < n^2, d, 1], {d, Divisors[n]}]; Array[a, 100] (* Amiram Eldar, Jun 08 2023 *)

Prog

(PARI) a(n) = vecprod(select(x->((sqrt(n)<x) && (x<n)), divisors(n))); \\ Michel Marcus, Jun 08 2023

Crossrefs

Cf. A007955, A007956, A072499, A363520.

Sequence in context: A302792 A179820 A364098 * A166050 A259655 A221185

Adjacent sequences: A363518 A363519 A363520 * A363522 A363523 A363524

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 07 2023

Status

approved