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Exponent of 2 in the prime factorization of (3n)!.
1

%I #11 Sep 01 2024 09:36:58

%S 1,4,7,10,11,16,18,22,23,26,31,34,35,39,41,46,47,50,53,56,57,64,66,70,

%T 71,74,78,81,82,86,88,94,95,98,101,104,105,110,112,116,117,120,127,

%U 130,131,135,137,142,143,146,149,152,153,159,161,165,166

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

%H Amiram Eldar, <a href="/A087298/b087298.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) = A011371(3*n) = 3*n - A036555(n). - _Amiram Eldar_, Sep 01 2024

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

%t a[n_] := 3*n - DigitCount[3*n, 2, 1]; Array[a, 100] (* _Amiram Eldar_, Sep 01 2024 *)

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

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

%K nonn,easy

%O 1,2

%A _Ralf Stephan_, Oct 20 2003