A292392 Numbers n such that n^2 divides (17^n + 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

Offset: 1

Author

K. D. Bajpai, Sep 15 2017

Keywords

• nonn

Comments

After a(1), all the terms are multiples of 3.

From Robert Israel, Sep 18 2017: (Start)

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)

Examples

			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.
		

Crossrefs

Cf. A015951, A123047, A123052, A177813, A292331.

Programs

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] &]

PARI

for(n=1, 5e6, if (Mod(17, n^2)^n==-1, print1(n, ", ")));

PARI

is(n) = Mod(17, n^2)^n==-1 \\ Felix Fröhlich, Sep 16 2017