%I #25 May 06 2020 15:43:05
%S 1,1,1,4,1,3,1,8,9,5,1,12,1,7,15,16,1,9,1,20,7,11,1,24,25,13,27,28,1,
%T 15,1,32,33,17,35,36,1,19,13,40,1,21,1,44,45,23,1,48,49,25,51,52,1,27,
%U 55,56,19,29,1,60,1,31,63,64,65,33,1,68,69,35,1,72,1
%N Denominator of (Sum(m^(n-1),m=1..n-1)+1)/n.
%C It is conjectured that this is 1 iff n is 1 or a prime.
%D R. K. Guy, Unsolved Problems in Number Theory, A17.
%H Robert Israel, <a href="/A055032/b055032.txt">Table of n, a(n) for n = 1..10000</a>
%p a:= proc(n) local S,m;
%p S:= 1;
%p for m from 1 to n-1 do
%p S:= S + m &^(n-1) mod n;
%p od:
%p denom(S/n);
%p end proc;
%p seq(a(n),n=1..1000); # _Robert Israel_, May 30 2014
%t Table[Denominator[(Sum[m^(n - 1), {m, 1, n - 1}] + 1)/n], {n, 1, 10}] (* _G. C. Greubel_, Jun 06 2016 *)
%o (PARI) a(n) = denominator((sum(m=1, n - 1, m^(n - 1)) + 1)/n); \\ _Indranil Ghosh_, May 17 2017
%o (Python)
%o from sympy import Integer
%o def a(n): return ((sum(m**(n - 1) for m in range(1, n)) + 1)/Integer(n)).denominator() # _Indranil Ghosh_, May 17 2017
%Y Cf. A055031, A055030, A055023, A201560, A204187.
%K nonn,frac
%O 1,4
%A _N. J. A. Sloane_, Jun 11 2000