A324465 Exponent of highest power of 2 that divides A324152(n).

0, 0, 1, 3, 2, 2, 3, 5, 2, 3, 4, 6, 5, 4, 5, 7, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 6, 7, 9, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 7, 8, 10, 5, 6, 7, 9, 8, 8, 9, 11, 8, 9, 10, 12, 11, 8, 9, 11, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 7, 8, 10, 5, 6, 7, 9

Offset: 0

Author

N. J. A. Sloane, Mar 01 2019

Keywords

• nonn

Comments

First occurrence of k=0,1,2,...: 0, 2, 4, 3, 10, 7, 11, 15, 23, 27, 47, 55, 59, 111, 119, 123, 239, 247, 251, 495, 503, 507, 1007, 1015, 1019, 2031, 2039, 2043, 4079, 4087, 4091, 8175, 8183, 8187, 16367, 16375, 16379, 32751, 32759, 32763, 65519, 65527, 65531, 131055, 131063, 131067, ..., . Robert G. Wilson v, Mar 01 2019

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (first 501 terms from N. J. A. Sloane)

Crossrefs

Cf. A000120 (binary weight), A007814, A324152, A324467.

Programs

Mathematica

f[n_] := IntegerExponent[(3/((n + 1)(n + 2)(n + 3)))*Multinomial[n, n, n, n], 2]; f[0] = 0; Array[f, 84, 0] (* Robert G. Wilson v, Mar 01 2019 *)

PARI

a(n) = 3*hammingweight(n) - valuation((n+1)*(n+2)*(n+3), 2); \\ Michel Marcus, Jul 10 2022

Formula

a(n) = 3*wt(n) - (2-adic valuation of (n+1)*(n+2)*(n+3))

= 3*A000120(n) - (A007814(n+1)+A007814(n+2)+A007814(n+3)).

E.g. if n = 14 = 1110_2, with weight 3, we get a(14) = 3*3 - 2-adic valuation of 15*16*17 = 9 - 4 = 5.