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%I #11 Jul 06 2022 16:59:48
%S 0,0,1,3,5,6,7,10,10,11,12,14,16,17,17,21,25,26,27,29,29,30,31,34,34,
%T 35,35,37,39,40,41,46,46,47,47,49,51,52,52,55,58,59,60,62,62,63,64,68,
%U 68,69,69,71,73,74,74,77,77,78,79,81,83,84,84,90,90,91,92,94,94,95,96
%N Powers of 2 in phi(n!).
%F a(n) = A007814(A048855(n)) = A007814(A000010(n!)).
%e For n=8, 8! = 40320 = 128*315, phi(40320) = 9216 = 9*1024, so a(8)=10, while the exponent of 2 in 8! is only 7. Exponents of 2 are larger in phi(n!) than in n!.
%o (Python)
%o from math import factorial, prod
%o from sympy import primerange
%o from fractions import Fraction
%o def A055597(n): return (~(m:=(factorial(n)*prod(Fraction(p-1,p) for p in primerange(n+1))).numerator)&m-1).bit_length() # _Chai Wah Wu_, Jul 06 2022
%Y Cf. A000010, A000720, A007814, A011371, A048855.
%K nonn
%O 1,4
%A _Labos Elemer_, Jul 11 2000
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