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%I #25 May 07 2020 16:30:58
%S 1,1,1,1,1,1,1,1,1,1,1,3,1,1,3,1,1,1,1,3,3,1,1,5,1,1,1,3,1,1,1,1,3,1,
%T 3,1,1,1,3,5,1,1,1,3,1,1,1,17,1,1,3,3,1,1,3,5,3,1,1,85,1,1,7,1,15,1,1,
%U 3,3,1,1,1,1,1,1,3,3,1,1,17,1,1,1,325,15,1,3,5,1,1,21,3,3,1,3,257,1,1,1,1
%N Denominator of Product_{d|n} b(d)^Moebius(n/d), where b() = A100371().
%H Vincenzo Librandi, <a href="/A226306/b226306.txt">Table of n, a(n) for n = 1..5000</a>
%H N. Bliss, B. Fulan, S. Lovett, and J. Sommars, <a href="http://dx.doi.org/10.4169/amer.math.monthly.120.06.519">Strong Divisibility, Cyclotomic Polynomials, and Iterated Polynomials</a>, Amer. Math. Monthly, 120 (2013), 519-536.
%e 1, 1, 3, 3, 15, 1, 63, 5, 21, 1, 1023, 5/3, 4095, 1, 17/3, 17, 65535, 1, 262143, 17/3, 65/3, 1, 4194303, 17/5, 69905, 1, 4161, 65/3, 268435455, 1, 1073741823, 257, 1025/3, 1, 53261/3, 13, ...
%t Table[Denominator[Product[(2^EulerPhi[d] - 1)^MoebiusMu[n/d], {d, Divisors[n]}]], {n, 100}] (* _Indranil Ghosh_, Apr 14 2017 *)
%o (Python)
%o from sympy import divisors, totient, mobius, prod
%o def a(n): return prod((2**totient(d) - 1)**mobius(n//d) for d in divisors(n)).denominator()
%o print([a(n) for n in range(1, 51)]) # _Indranil Ghosh_, Apr 14 2017
%Y Cf. A100371, A226305.
%K nonn,frac
%O 1,12
%A _N. J. A. Sloane_, Jun 07 2013
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