A045576 Numbers k that divide 3^k + 2^k.

1, 5, 25, 55, 125, 275, 605, 625, 1375, 3025, 3125, 6655, 6875, 15125, 15625, 30025, 31375, 33275, 34375, 73205, 75625, 78125, 150125, 156875, 166375, 171875, 330275, 345125, 366025, 378125, 390625, 439835, 750625, 784375, 805255, 831875

Offset

1,2

Comments

For any j>=0, 5*A003598(j) is a term of the sequence. - Benoit Cloitre, Mar 08 2002

From Robert Israel, Jun 29 2017: (Start)

This is a semigroup: if m and n are in the sequence, then so is m*n.

If n is in the sequence and is divisible by prime p, then so is p*n.

The only prime power in the sequence is 5.

Conjecture: Every member of the sequence except 1 is of the form p*m where p is prime and m is in the sequence. (End)

Links

Robert Israel and Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 205 terms from Robert Israel)

Maple

select(t -> 3 &^ t + 2 &^ t mod t = 0, [seq(i, i=1..10^6, 2)]); # Robert Israel, Jun 29 2017

Prog

(PARI) isok(n) = ((3^n+2^n) % n) == 0; \\ Michel Marcus, Jun 29 2017
(PARI) isok(n)=(Mod(2, n)^n+Mod(3, n)^n)==0; \\ significantly more efficient
for(n=1, 10^6, if(isok(n), print1(n, ", "))); \\ Joerg Arndt, Aug 13 2017

Crossrefs

Cf. A003598, A007689.

Sequence in context: A078569 A044082 A161143 * A146649 A326314 A273357

Adjacent sequences: A045573 A045574 A045575 * A045577 A045578 A045579

Keyword

nonn

Author

David W. Wilson

Status

approved