A225101 - OEIS

%I #28 Nov 22 2023 22:42:01

%S 0,1,2,7,6,31,18,127,170,511,186,2047,630,8191,10922,32767,7710,

%T 131071,27594,524287,699050,2097151,364722,8388607,6710886,33554431,

%U 44739242,19173961,18512790,536870911,69273666,2147483647,2863311530,8589934591,34359738366,34359738367,3714566310

%N Numerator of (2^n - 2)/n.

%C That (2^n - 2)/n is an integer when n is prime can easily be proved as a simple consequence of Fermat's little theorem.

%C It was believed long ago that (2^n - 2)/n is an integer only when n = 1 or a prime. In 1819, Frédéric Sarrus found the smallest counterexample, 341; these pseudoprimes are now sometimes called "Sarrus numbers" (A001567).

%D Alkiviadis G. Akritas, Elements of Computer Algebra With Application. New York: John Wiley & Sons (1989): 66.

%D George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press, 1982, p. 22.

%H Colin Barker, <a href="/A225101/b225101.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChineseHypothesis.html">Chinese Hypothesis</a>

%e a(4) = 7 because (2^4 - 2)/4 = 7/2.

%e a(5) = 6 because (2^5 - 2)/5 = 6.

%e a(6) = 31 because (2^6 - 2)/6 = 31/3.

%p A225101:=n->numer((2^n-2)/n): seq(A225101(n), n=1..50); # _Wesley Ivan Hurt_, Nov 10 2014

%t Table[Numerator[(2^n - 2)/n], {n, 50}]

%o (PARI) vector(100, n, numerator((2^n - 2)/n)) \\ _Colin Barker_, Nov 09 2014

%o (Magma) [Numerator((2^n - 2)/n): n in  [1..60]]; // _Vincenzo Librandi_, Nov 09 2014

%Y Cf. A001567, A064535, A159353 (denominators).

%K easy,nonn,frac

%O 1,3

%A _Alonso del Arte_, Apr 28 2013