cp's OEIS Frontend

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

%I A181572 #23 Sep 08 2022 08:45:54
%S A181572 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,
%T A181572 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,
%U A181572 6,5,4,4,7,7,4,4,5,6,8,6,3,3,6,3,9,5,4
%N A181572 Number of distinct prime divisors of 5^n + n.
%C A181572 5^n + n is composite for all n < 1000. - Pete L. Clark ( Department of Mathematics University of Georgia).
%C A181572 5^7954 + 7954 has been found to be prime by a computer (see Links).
%H A181572 Amiram Eldar, <a href="/A181572/b181572.txt">Table of n, a(n) for n = 1..182</a>
%H A181572 5^n+n is never prime? <a href="http://math.stackexchange.com/questions/4125/5nn-is-never-prime">5^n+n is never prime?</a>
%H A181572 Mersenneforum.org discussion, <a href="http://www.mersenneforum.org/showpost.php?p=233370">5^7954 + 7954 has been found to be prime by a computer</a>
%F A181572 a(n) = A001221(A104745(n)). - _Amiram Eldar_, Feb 19 2020
%e A181572 a(5) = 3 because 5^5 + 5 = 2*5*313 has 3 prime factors.
%p A181572 with(numtheory):for n from 1 to 100 do:x:=5^n + n: y:=nops(factorset(x)):printf(`%d,  `,y):od:
%t A181572 PrimeNu/@Table[5^n+n,{n,20}] (* _Harvey P. Dale_, Feb 17 2013 *)
%o A181572 (PARI) a(n)=omega(5^n+n) \\ _Charles R Greathouse IV_, Aug 27 2014
%o A181572 (Magma) [#PrimeDivisors(5^n+n): n in [1..107]]; // _Marius A. Burtea_, Feb 19 2020
%Y A181572 Cf. A001221, A104745.
%K A181572 nonn
%O A181572 1,1
%A A181572 _Michel Lagneau_, Jan 30 2011
%E A181572 a(71)-a(87) from _Amiram Eldar_, Feb 19 2020