A096125 Least value of k such that n!/((n-k)!)^2 is an integer.

1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 13, 14, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 26, 27, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38

Offset: 1

Author

Amarnath Murthy, Jul 01 2004

Keywords

• nonn

Comments

If p is the first prime > n/2, then a(n) > n-p. - Robert Israel, Jun 27 2018

Examples

			a(10) = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096123, A096124.

Programs

Maple

f:= proc(n) local p,k;
  p:= nextprime(floor(n/2));
  for k from n-p+1 do
    if (n!/((n-k)!)^2)::integer then return k fi
  od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Jun 27 2018

Mathematica

f[n_] := Block[{i = 1, t = Table[n!/(n - k)!^2, {k, n}]}, While[ !IntegerQ[ t[[i]]], i++ ]; i]; Table[ f[n], {n, 75}] (* Robert G. Wilson v, Jul 03 2004 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jul 03 2004