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A055032 Denominator of (Sum(m^(n-1),m=1..n-1)+1)/n.

%I A055032 #28 Jun 27 2025 09:29:22
%S A055032 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 A055032 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 A055032 55,56,19,29,1,60,1,31,63,64,65,33,1,68,69,35,1,72,1
%N A055032 Denominator of (Sum(m^(n-1),m=1..n-1)+1)/n.
%C A055032 It is conjectured that this is 1 iff n is 1 or a prime.
%D A055032 R. K. Guy, Unsolved Problems in Number Theory, A17.
%H A055032 Robert Israel, <a href="/A055032/b055032.txt">Table of n, a(n) for n = 1..10000</a>
%p A055032 a:= proc(n) local S,m;
%p A055032     S:= 1;
%p A055032     for m from 1 to n-1 do
%p A055032       S:= S + m &^(n-1) mod n;
%p A055032     od:
%p A055032     denom(S/n);
%p A055032 end proc;
%p A055032 seq(a(n),n=1..1000); # _Robert Israel_, May 30 2014
%t A055032 Table[Denominator[(Sum[m^(n - 1), {m, 1, n - 1}] + 1)/n], {n, 1, 10}] (* _G. C. Greubel_, Jun 06 2016 *)
%o A055032 (PARI) a(n) = denominator((sum(m=1, n - 1, m^(n - 1)) + 1)/n); \\ _Indranil Ghosh_, May 17 2017
%o A055032 (Python)
%o A055032 from sympy import Integer
%o A055032 def a(n): return ((sum(m**(n - 1) for m in range(1, n)) + 1)/Integer(n)).denominator # _Indranil Ghosh_, May 17 2017
%Y A055032 Cf. A055031, A055030, A055023, A201560, A204187.
%K A055032 nonn,frac
%O A055032 1,4
%A A055032 _N. J. A. Sloane_, Jun 11 2000