A170826 a(n) = gcd(n^2, n!).

1, 2, 3, 8, 5, 36, 7, 64, 81, 100, 11, 144, 13, 196, 225, 256, 17, 324, 19, 400, 441, 484, 23, 576, 625, 676, 729, 784, 29, 900, 31, 1024, 1089, 1156, 1225, 1296, 37, 1444, 1521, 1600, 41, 1764, 43, 1936, 2025, 2116, 47, 2304, 2401, 2500, 2601, 2704, 53, 2916

Offset: 1

Author

N. J. A. Sloane, Dec 27 2009

Keywords

• nonn
• easy

Crossrefs

Cf. A010051, A092043.

Programs

Maple

GCDWITHFACTORIAL:=proc(a) local b,i,k:
if whattype(a) <> list then RETURN([]); fi:
b:=[]:
for i to nops(a) do b:=[op(b), gcd(a[i],i!)]: od;
RETURN(b);
end:
A170826 := proc(n): gcd(n^2, n!) end: seq(A170826(n), n=1..54); # Johannes W. Meijer, Jun 04 2016

Mathematica

Table[GCD[n^2, n!], {n, 54}] (* Michael De Vlieger, Jun 05 2016 *)

PARI

a(n)=if(isprime(n),n,if(n==4,8,n^2)) \\ Charles R Greathouse IV, Feb 01 2013

Formula

If n is prime then a(n) = n; otherwise, if n <> 4 then a(n) = n^2. - Zak Seidov, Dec 28 2009

a(n) = n!/A092043(n). - Johannes W. Meijer, Jun 04 2016

a(n) = n^2 / n^c(n), where c = A010051 for n >= 5. - Wesley Ivan Hurt, Nov 10 2023