A175417 Exponent of 2 minus sum of all other exponents, in the prime power factorization of n!

0, 0, 1, 0, 2, 1, 1, 0, 3, 1, 1, 0, 1, 0, 0, -2, 2, 1, 0, -1, 0, -2, -2, -3, -1, -3, -3, -6, -5, -6, -7, -8, -3, -5, -5, -7, -7, -8, -8, -10, -8, -9, -10, -11, -10, -13, -13, -14, -11, -13, -14, -16, -15, -16, -18, -20, -18, -20, -20, -21, -21, -22, -22, -25, -19, -21, -22

Offset

0,5

Comments

a(n)=0 for n={0,1,3,7,11,13,14,18,20}.

Links

Table of n, a(n) for n=0..66.

Formula

a(n)=2*A011371(n)-A022559(n).

Example

a(20) = 0 because 20! = 2432902008176640000 = ((2^18)*(3^8)*(5^4)*(7^2)*(11^1)*(13^1)*(17^1)*(19^1)) and 18-(8+4+2+1+1+1+1) = 0.

Mathematica

Table[2*IntegerExponent[m!, 2]-Total[Last/@FactorInteger[m! ]], {m, 0, 130}]

Crossrefs

Cf. A000142, A011371, A027868, A054861, A054896.

Sequence in context: A128589 A130162 A175595 * A136481 A100218 A098599

Adjacent sequences: A175414 A175415 A175416 * A175418 A175419 A175420

Keyword

sign

Author

Zak Seidov, May 08 2010

Status

approved