|
|
A055032
|
|
Denominator of (Sum(m^(n-1),m=1..n-1)+1)/n.
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
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
|
|
|
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;
|
|
MATHEMATICA
|
Table[Denominator[(Sum[m^(n - 1), {m, 1, n - 1}] + 1)/n], {n, 1, 10}] (* G. C. Greubel, Jun 06 2016 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|