A045590 Numbers k that divide 5^k + 4^k.

1, 3, 9, 21, 27, 63, 81, 147, 189, 243, 441, 567, 729, 903, 1029, 1323, 1701, 2187, 2667, 2709, 2943, 3087, 3969, 5103, 6321, 6561, 7203, 8001, 8127, 8829, 9261, 11907, 13203, 15309, 18669, 18963, 19683, 20601, 21609, 24003, 24381, 26487

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

From Robert Israel, May 19 2025: (Start)

All terms are coprime to 10.

The only prime term is 3.

If k is a term, then so is 3 * k.

Is 1 the only term not divisible by 3? (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A074611.

Programs

Maple

filter:= k -> 5 &^ k + 4 &^ k mod k = 0:
select(filter, [seq(i,i=1..10^5,2)]); # Robert Israel, May 19 2025

Mathematica

Select[Range[30000],Divisible[5^#+4^#,#]&] (* Harvey P. Dale, Nov 17 2013 *)