A181861 a(n) = gcd(n^2, n!/floor(n/2)!^2).

1, 1, 2, 3, 2, 5, 4, 7, 2, 9, 4, 11, 12, 13, 4, 45, 2, 17, 4, 19, 4, 21, 4, 23, 4, 25, 4, 27, 8, 29, 180, 31, 2, 99, 4, 175, 12, 37, 4, 117, 20, 41, 12, 43, 8, 675, 4, 47, 36, 49, 4, 153, 8, 53, 4, 55, 56, 57, 4, 59, 16

Offset

0,3

Links

Marius A. Burtea, Table of n, a(n) for n = 0..1000

Formula

a(n) = gcd(A000290(n), A056040(n)).

a(2^k) = 2 for k>0. If p is an odd prime, then a(p^k) = p^k. - Chai Wah Wu, May 08 2026

Maple

A181861 := n -> igcd(n^2, n!/iquo(n, 2)!^2);

Mathematica

sf[n_] := n!/Quotient[n, 2]!^2; Table[GCD[n^2, sf[n]], {n, 0, 60}] (* Jean-François Alcover, Jun 28 2013 *)

Prog

(PARI) a(n)=gcd(n!/(n\2)!^2, n^2) \\ Charles R Greathouse IV, Feb 01 2013
(Magma) [Gcd(n^2, Floor(Factorial(n)/(Factorial(Floor(n/2))^2))):n in [0..60]]; // Marius A. Burtea, Aug 03 2019
(Python)
from math import prod
from sympy import factorint
from sympy.ntheory.factor_ import digits
def A181861(n):
    def s(n, p): return sum(digits(n, p)[1:])
    return prod(p**min(e<<1, ((n-(n&-2))+(s(n>>1, p)<<1)-s(n, p))//(p-1)) for p, e, in factorint(n).items()) if n else 1 # Chai Wah Wu, May 05 2026

Crossrefs

Cf. A170826, A181860, A056040, A000290.

Sequence in context: A367580 A195637 A383535 * A365099 A342694 A212831

Adjacent sequences: A181858 A181859 A181860 * A181862 A181863 A181864

Keyword

nonn

Author

Peter Luschny, Nov 21 2010

Status

approved