A181858 - OEIS

A181858

a(n) = lcm(n^2, n!) / lcm(n^2, swinging_factorial(n)).

1, 1, 1, 1, 1, 4, 4, 36, 18, 64, 576, 14400, 43200, 518400, 518400, 5080320, 12700800, 1625702400, 1625702400, 131681894400, 131681894400, 627056640000, 13168189440000, 1593350922240000

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OFFSET

0,6

COMMENTS

A divisibility sequence, i.e., if m|n then a(m)|a(n). Except for n = 9 the prime factors of A181858(n) are the primes <= floor((n-1)/2). Using this fact the divisibility property can be proved. - Peter Luschny, Jan 10 2011

LINKS

Table of n, a(n) for n=0..23.

Index to divisibility sequences

FORMULA

a(n) = A181857(n) / A181860(n).

MAPLE

A181858 := n -> `if`(n=0, 1, ilcm(n^2, n!)/ilcm(n^2, n!/iquo(n, 2)!^2));

MATHEMATICA

a[n_] := If[n == 0, 1, LCM[n^2, n!]/LCM[n^2, n!/Quotient[n, 2]!^2]];

Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 18 2019 *)

PROG

(PARI) a(n)=lcm(n^2, n!)/lcm(n!/(n\2)!^2, n^2) \\ Charles R Greathouse IV, Feb 01 2013