A226306 Denominator of Product_{d|n} b(d)^Moebius(n/d), where b() = A100371().
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, 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, 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
Offset: 1
Examples
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, ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..5000
- N. Bliss, B. Fulan, S. Lovett, and J. Sommars, Strong Divisibility, Cyclotomic Polynomials, and Iterated Polynomials, Amer. Math. Monthly, 120 (2013), 519-536.
Programs
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Mathematica
Table[Denominator[Product[(2^EulerPhi[d] - 1)^MoebiusMu[n/d], {d, Divisors[n]}]], {n, 100}] (* Indranil Ghosh, Apr 14 2017 *) -
Python
from sympy import divisors, totient, mobius, prod def a(n): return prod((2**totient(d) - 1)**mobius(n//d) for d in divisors(n)).denominator print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Apr 14 2017