A181572 Number of distinct prime divisors of 5^n + n.

2, 1, 1, 2, 3, 3, 4, 2, 3, 4, 3, 3, 3, 5, 5, 3, 2, 5, 4, 4, 4, 3, 2, 3, 5, 3, 4, 4, 5, 5, 4, 3, 3, 4, 4, 3, 5, 5, 4, 9, 3, 6, 6, 5, 4, 6, 3, 4, 5, 4, 3, 5, 5, 4, 9, 2, 5, 4, 4, 6, 7, 4, 3, 6, 7, 4, 7, 4, 6, 5, 4, 4, 7, 7, 4, 4, 5, 6, 8, 6, 3, 3, 6, 3, 9, 5, 4

Offset

1,1

Comments

5^n + n is composite for all n < 1000. - Pete L. Clark ( Department of Mathematics University of Georgia).

5^7954 + 7954 has been found to be prime by a computer (see Links).

Links

Amiram Eldar, Table of n, a(n) for n = 1..182

5^n+n is never prime? 5^n+n is never prime?

Mersenneforum.org discussion, 5^7954 + 7954 has been found to be prime by a computer

Formula

a(n) = A001221(A104745(n)). - Amiram Eldar, Feb 19 2020

Example

a(5) = 3 because 5^5 + 5 = 2*5*313 has 3 prime factors.

Maple

with(numtheory):for n from 1 to 100 do:x:=5^n + n: y:=nops(factorset(x)):printf(`%d,  `, y):od:

Mathematica

PrimeNu/@Table[5^n+n, {n, 20}] (* Harvey P. Dale, Feb 17 2013 *)

Prog

(PARI) a(n)=omega(5^n+n) \\ Charles R Greathouse IV, Aug 27 2014
(Magma) [#PrimeDivisors(5^n+n): n in [1..107]]; // Marius A. Burtea, Feb 19 2020

Crossrefs

Cf. A001221, A104745.

Sequence in context: A073725 A055223 A174807 * A287731 A289816 A363148

Adjacent sequences: A181569 A181570 A181571 * A181573 A181574 A181575

Keyword

nonn

Author

Michel Lagneau, Jan 30 2011

Extensions

a(71)-a(87) from Amiram Eldar, Feb 19 2020

Status

approved