A157279 - OEIS

%I #6 Sep 08 2022 08:45:41

%S 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,

%T 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,

%U 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

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

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

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

%t Table[Mod[Floor[Sqrt[n]]!,n],{n,90}] (* _Harvey P. Dale_, Feb 15 2022 *)

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

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

%K nonn

%O 1,4

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

%E Edited and a(1) corrected by _Klaus Brockhaus_, May 27 2009