A157279 Product 1*2*...*r mod n, where r = integer part of sqrt(n).

0, 1, 1, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 8, 7, 6, 5, 4, 3, 2, 1, 0, 20, 16, 12, 8, 4, 0, 27, 24, 21, 18, 15, 0, 17, 36, 18, 0, 23, 6, 32, 16, 0, 30, 15, 0, 42, 40, 42, 48, 5, 18, 35, 0, 24, 52, 25, 0, 38, 18, 0, 0, 20, 60, 53, 64, 24, 0, 63, 0, 24, 64, 45, 40, 49, 72, 30, 0, 0, 30, 4, 0

Offset: 1

Author

Thomas Kerscher (Thomas.Kerscher(AT)web.de), Feb 26 2009

Keywords

• nonn

Examples

			a(17) = (floor(sqrt(17)))! mod 17 = (floor(4.12...))! mod 17 = 4! mod 17 = 24 mod 17 = 7.
		

Crossrefs

Cf. A000142 (factorial numbers), A000196 (integer part of square root of n).

Programs

Magma

[ Factorial(Floor(Sqrt(n))) mod n: n in [1..84] ];

Mathematica

Table[Mod[Floor[Sqrt[n]]!,n],{n,90}] (* Harvey P. Dale, Feb 15 2022 *)

Formula

a(n) = (floor(sqrt(n)))! mod n.

Extensions

Edited and a(1) corrected by Klaus Brockhaus, May 27 2009