A128474 - OEIS

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

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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