cp's OEIS Frontend

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

%I A096125 #10 Jun 28 2018 02:50:13
%S A096125 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,
%T A096125 15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,
%U A096125 27,26,27,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36,37,37,38
%N A096125 Least value of k such that n!/((n-k)!)^2 is an integer.
%C A096125 If p is the first prime > n/2, then a(n) > n-p. - _Robert Israel_, Jun 27 2018
%H A096125 Robert Israel, <a href="/A096125/b096125.txt">Table of n, a(n) for n = 1..10000</a>
%e A096125 a(10) = 4.
%p A096125 f:= proc(n) local p,k;
%p A096125   p:= nextprime(floor(n/2));
%p A096125   for k from n-p+1 do
%p A096125     if (n!/((n-k)!)^2)::integer then return k fi
%p A096125   od
%p A096125 end proc:
%p A096125 f(1):= 1:
%p A096125 map(f, [$1..100]); # _Robert Israel_, Jun 27 2018
%t A096125 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 *)
%Y A096125 Cf. A096123, A096124.
%K A096125 nonn
%O A096125 1,3
%A A096125 _Amarnath Murthy_, Jul 01 2004
%E A096125 Edited, corrected and extended by _Robert G. Wilson v_, Jul 03 2004