This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A055597 #17 Jul 12 2024 10:16:58 %S A055597 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 A055597 35,35,37,39,40,41,46,46,47,47,49,51,52,52,55,58,59,60,62,62,63,64,68, %U A055597 68,69,69,71,73,74,74,77,77,78,79,81,83,84,84,90,90,91,92,94,94,95,96 %N A055597 Exponent of the highest power of 2 dividing phi(n!). %H A055597 Amiram Eldar, <a href="/A055597/b055597.txt">Table of n, a(n) for n = 1..10000</a> %F A055597 a(n) = A007814(A048855(n)) = A007814(A000010(n!)). %e A055597 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!. %t A055597 a[n_] := IntegerExponent[EulerPhi[n!], 2]; Array[a, 100] (* _Amiram Eldar_, Jul 12 2024 *) %o A055597 (Python) %o A055597 from math import factorial, prod %o A055597 from sympy import primerange %o A055597 from fractions import Fraction %o A055597 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 %o A055597 (PARI) a(n) = valuation(eulerphi(n!), 2); \\ _Amiram Eldar_, Jul 12 2024 %Y A055597 Cf. A000010, A000720, A007814, A011371, A048855. %K A055597 nonn %O A055597 1,4 %A A055597 _Labos Elemer_, Jul 11 2000 %E A055597 Name clarified by _Amiram Eldar_, Jul 12 2024