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

Author

Michel Lagneau, Jan 30 2011

Keywords

• nonn

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).

Examples

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

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

Crossrefs

Cf. A001221, A104745.

Programs

Magma

[#PrimeDivisors(5^n+n): n in [1..107]]; // Marius A. Burtea, Feb 19 2020

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 *)

PARI

a(n)=omega(5^n+n) \\ Charles R Greathouse IV, Aug 27 2014

Formula

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

Extensions

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