A069927 Numbers k that divide 2^(k+3) - 1.

1, 3, 5, 9, 21, 45, 63, 85, 105, 117, 273, 285, 357, 585, 627, 765, 1365, 1397, 1449, 1677, 1989, 2337, 3597, 3705, 3885, 4221, 4365, 4485, 4797, 4953, 5061, 5607, 5797, 7137, 7521, 7565, 7665, 8109, 10197, 10545, 10845, 11445, 11565, 12597, 13065, 13717, 14637

Offset: 1

Author

Benoit Cloitre, Apr 25 2002

Keywords

• easy
• nonn

Examples

			k = 1 divides 2^(k+3) - 1 = 15, so 1 is a term.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 500 terms from Harvey P. Dale)

Crossrefs

Cf. A187787.

Programs

Maple

q:= k-> 0=(2&^(k+3)-1) mod k:
select(q, [$1..20000])[];  # Alois P. Heinz, Apr 10 2025

Mathematica

Select[Range[15000],PowerMod[2,#+3,#]==1&] (* Harvey P. Dale, Jul 09 2018 *)

Extensions

Missing term 1 inserted by Alois P. Heinz, Apr 10 2025