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 A175417 Exponent of 2 minus sum of all other exponents, in the prime power factorization of n! 0

%I

%S 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,

%T -6,-7,-8,-3,-5,-5,-7,-7,-8,-8,-10,-8,-9,-10,-11,-10,-13,-13,-14,-11,

%U -13,-14,-16,-15,-16,-18,-20,-18,-20,-20,-21,-21,-22,-22,-25,-19,-21,-22

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

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

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

%e 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.

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

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

%K sign

%O 0,5

%A _Zak Seidov_, May 08 2010

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Last modified July 22 14:41 EDT 2019. Contains 325222 sequences. (Running on oeis4.)