OFFSET
1,4
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
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!.
MATHEMATICA
a[n_] := IntegerExponent[EulerPhi[n!], 2]; Array[a, 100] (* Amiram Eldar, Jul 12 2024 *)
PROG
(Python)
from math import factorial, prod
from sympy import primerange
from fractions import Fraction
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
(PARI) a(n) = valuation(eulerphi(n!), 2); \\ Amiram Eldar, Jul 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 11 2000
EXTENSIONS
Name clarified by Amiram Eldar, Jul 12 2024
STATUS
approved