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 A096125 Least value of k such that n!/((n-k)!)^2 is an integer. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If p is the first prime > n/2, then a(n) > n-p. - Robert Israel, Jun 27 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(10) = 4. 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 *) CROSSREFS Cf. A096123, A096124. Sequence in context: A167232 A319468 A137791 * A140828 A262907 A341721 Adjacent sequences:  A096122 A096123 A096124 * A096126 A096127 A096128 KEYWORD nonn AUTHOR Amarnath Murthy, Jul 01 2004 EXTENSIONS Edited, corrected and extended by Robert G. Wilson v, Jul 03 2004 STATUS approved

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Last modified January 21 20:28 EST 2022. Contains 350480 sequences. (Running on oeis4.)