A181899 Largest divisor of n!/4 which is less than sqrt(n!)/2.

2, 5, 12, 35, 96, 288, 945, 3150, 10800, 39312, 147420, 571536, 2286144, 9424800, 39984000, 174283200, 779688000, 3573570000, 16761064320, 80379048750, 393826406400, 1969132032000, 10040487256800, 52174220175000, 276080056560000, 1486750296281250

Offset: 4

Author

Artur Jasinski, Mar 31 2012

Keywords

• nonn

Comments

Comment from A038202: Let f=n!/4 and let a(n) be the largest divisor of f such that a(n) < sqrt(f). Then A038202(n) = f/a(n) - a(n). The greatest k such that n!+k^2 is a square is f-1. The number of k for which n!+k^2 is a square is A038548(f). - T. D. Noe, Nov 02 2004

Crossrefs

Cf. A038202, A138196, A139151, A181892, A181893.

Programs

Mathematica

Table[f = n!/4; Select[Divisors[f], # <= Sqrt[f] &][[-1]], {n, 4, 20}]