A363520 Product of the divisors of n that are < sqrt(n).

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 8, 3, 2, 1, 24, 1, 2, 3, 8, 1, 30, 1, 8, 3, 2, 5, 24, 1, 2, 3, 40, 1, 36, 1, 8, 15, 2, 1, 144, 1, 10, 3, 8, 1, 36, 5, 56, 3, 2, 1, 720, 1, 2, 21, 8, 5, 36, 1, 8, 3, 70, 1, 1152, 1, 2, 15, 8, 7, 36, 1, 320, 3, 2, 1

Offset

1,6

Links

Table of n, a(n) for n=1..83.

Formula

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

a(n) = Product_{k=1..floor(sqrt(n-1))} k^c(n/k), where c(m) = 1-ceiling(m)+floor(m).

a(n) = A072499(n)/A000196(n)^A010052(n) for n>=1.

Example

The product of divisors of 16 that are < sqrt(16) = 4 is 1*2 = 2, so a(16) = 2.

Mathematica

a[n_] := Times @@ Select[Divisors[n], #^2 < n &]; Array[a, 100]

Prog

(PARI) a(n) = vecprod(select(x->(x^2<n), divisors(n))); \\ Michel Marcus, Jun 08 2023

Crossrefs

Cf. A000196, A010052, A072499, A363521.

Cf. A070039 (sum of those divisors).

Sequence in context: A322401 A124333 A144757 * A215136 A318658 A318512

Adjacent sequences: A363517 A363518 A363519 * A363521 A363522 A363523

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 07 2023

Status

approved