A245087 Largest number such that 2^a(n) is a divisor of (n!)!.

0, 0, 1, 4, 22, 116, 716, 5034, 40314, 362874, 3628789, 39916793, 479001588, 6227020788, 87178291188, 1307674367982, 20922789887982, 355687428095978, 6402373705727977, 121645100408831983, 2432902008176639978, 51090942171709439975, 1124000727777607679972

Offset: 0

Author

Stanislav Sykora, Jul 15 2014

Keywords

• nonn

Comments

Also the number of trailing zeros in the binary expansion of (n!)!.

Examples

			a(4)=22 because (4!)!=620448401733239439360000 is divisible by 2^22 but not by 2^23.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..399

Crossrefs

Cf. A000120 (Hamming weights), A000142, A000197, A011371.

Programs

PARI

a(n) = n!-hammingweight(n!)

Formula

a(n) = n! - Hw(n!), Hw being the Hamming weight function.

a(n) = A011371(A000142(n)).