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

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, 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, 55, 56, 19, 29, 1, 60, 1, 31, 63, 64, 65, 33, 1, 68, 69, 35, 1, 72, 1

Offset: 1

Author

N. J. A. Sloane, Jun 11 2000

Keywords

• nonn
• frac

Comments

It is conjectured that this is 1 iff n is 1 or a prime.

References

• R. K. Guy, Unsolved Problems in Number Theory, A17.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055031, A055030, A055023, A201560, A204187.

Programs

Maple

a:= proc(n) local S,m;
    S:= 1;
    for m from 1 to n-1 do
      S:= S + m &^(n-1) mod n;
    od:
    denom(S/n);
end proc;
seq(a(n),n=1..1000); # Robert Israel, May 30 2014

Mathematica

Table[Denominator[(Sum[m^(n - 1), {m, 1, n - 1}] + 1)/n], {n, 1, 10}] (* G. C. Greubel, Jun 06 2016 *)

PARI

a(n) = denominator((sum(m=1, n - 1, m^(n - 1)) + 1)/n); \\ Indranil Ghosh, May 17 2017

Python

from sympy import Integer
def a(n): return ((sum(m**(n - 1) for m in range(1, n)) + 1)/Integer(n)).denominator # Indranil Ghosh, May 17 2017