

A181572


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


2



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
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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 A054482
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



