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

1,2

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A115566 A364840 A190507 * A237707 A211642 A127958

Adjacent sequences: A087295 A087296 A087297 * A087299 A087300 A087301

Keyword

nonn,easy

Author

Ralf Stephan, Oct 20 2003

Status

approved