A087298 Exponent of 2 in the prime factorization of (3n)!.

1, 4, 7, 10, 11, 16, 18, 22, 23, 26, 31, 34, 35, 39, 41, 46, 47, 50, 53, 56, 57, 64, 66, 70, 71, 74, 78, 81, 82, 86, 88, 94, 95, 98, 101, 104, 105, 110, 112, 116, 117, 120, 127, 130, 131, 135, 137, 142, 143, 146, 149, 152, 153, 159, 161, 165, 166

Offset: 1

Author

Ralf Stephan, Oct 20 2003

Keywords

• nonn
• easy

Examples

			(3*5)! = 2^11 * 638512875, so a(5) = 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011371 (n!), A005187 ((2n)!), A036555.

Programs

Mathematica

a[n_] := 3*n - DigitCount[3*n, 2, 1]; Array[a, 100] (* Amiram Eldar, Sep 01 2024 *)

PARI

a(n)=valuation((3*n)!,2)

Formula

a(2n) = a(n) + 3n.

a(n) = Sum_{k>=1} floor(3n/2^k).

a(n) = A011371(3*n) = 3*n - A036555(n). - Amiram Eldar, Sep 01 2024