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

0,4

Comments

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

Links

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

Formula

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

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

Example

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

Prog

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

Crossrefs

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

Sequence in context: A293966 A305554 A291183 * A155596 A244900 A261193

Adjacent sequences: A245084 A245085 A245086 * A245088 A245089 A245090

Keyword

nonn

Author

Stanislav Sykora, Jul 15 2014

Status

approved