OFFSET
1,3
COMMENTS
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.
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).
REFERENCES
Alkiviadis G. Akritas, Elements of Computer Algebra With Application. New York: John Wiley & Sons (1989): 66.
George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press, 1982, p. 22.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Chinese Hypothesis
EXAMPLE
a(4) = 7 because (2^4 - 2)/4 = 7/2.
a(5) = 6 because (2^5 - 2)/5 = 6.
a(6) = 31 because (2^6 - 2)/6 = 31/3.
MAPLE
MATHEMATICA
Table[Numerator[(2^n - 2)/n], {n, 50}]
PROG
(PARI) vector(100, n, numerator((2^n - 2)/n)) \\ Colin Barker, Nov 09 2014
(Magma) [Numerator((2^n - 2)/n): n in [1..60]]; // Vincenzo Librandi, Nov 09 2014
CROSSREFS
KEYWORD
easy,nonn,frac
AUTHOR
Alonso del Arte, Apr 28 2013
STATUS
approved