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

1,4

Links

Table of n, a(n) for n=1..84.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A343122 A338869 A104588 * A214080 A278241 A010671

Adjacent sequences: A157276 A157277 A157278 * A157280 A157281 A157282

Keyword

nonn

Author

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

Extensions

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

Status

approved