A128474 Largest number k such that 2^k divides n*(n-3)!.

0, 2, 1, 2, 3, 6, 4, 5, 7, 9, 8, 9, 10, 14, 11, 12, 15, 17, 16, 17, 18, 21, 19, 20, 22, 24, 23, 24, 25, 30, 26, 27, 31, 33, 32, 33, 34, 37, 35, 36, 38, 40, 39, 40, 41, 45, 42, 43, 46, 48, 47, 48, 49, 52, 50, 51, 53, 55, 54, 55, 56, 62, 57, 58, 63, 65, 64, 65, 66, 69, 67, 68, 70

Offset

3,2

Links

Table of n, a(n) for n=3..75.

Formula

a(n) = A007814(n) + A011371(n-3).

Mathematica

a[n_] := IntegerExponent[n, 2] + n - 3 - DigitCount[n - 3, 2, 1]; Array[a, 100, 3] (* Amiram Eldar, May 23 2024 *)

Prog

(PARI) a(n) = valuation(n, 2) + n - 3 - hammingweight(n-3); \\ Amiram Eldar, May 23 2024

Crossrefs

Cf. A007814, A011371.

Sequence in context: A198123 A106576 A301336 * A108618 A097719 A249050

Adjacent sequences: A128471 A128472 A128473 * A128475 A128476 A128477

Keyword

nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007

Status

approved