|
|
A292392
|
|
Numbers n such that n^2 divides (17^n + 1).
|
|
1
|
|
|
1, 3, 9, 21, 39, 63, 117, 273, 819, 2067, 3081, 6201, 9243, 12807, 14469, 21567, 43407, 48711, 50877, 64701, 89649, 146133, 149331, 163293, 166491, 221169, 340977, 356139, 447993, 489879, 546819, 661401, 663507, 1022931, 1143051, 1165437, 1548183, 1639911, 1640457
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
After a(1), all the terms are multiples of 3.
All terms are odd.
If m and n are terms then lcm(m,n) is a term.
If n is a term not divisible by 9, then 3n is a term. (End)
|
|
LINKS
|
|
|
EXAMPLE
|
3 appears is a term because 3^2 divides (17^3 + 1): 4914/9 = 546.
9 appears is a term because 9^2 divides (17^9 + 1): 118587876498/81 = 1464047858.
|
|
MAPLE
|
A292392:= proc(n) if(17 &^ n+1)mod (n^2)=0 then RETURN (n); fi; end: seq(A292392(n), n=1..50000);
|
|
MATHEMATICA
|
Select[Range[50000], IntegerQ[(PowerMod[17, #, #^2] + 1)/#^2] &]
|
|
PROG
|
(PARI) for(n=1, 5e6, if (Mod(17, n^2)^n==-1, print1(n, ", ")));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|