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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
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
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
Sequence in context: A055223 A174807 A376939 * A287731 A289816 A374412
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 30 2011
EXTENSIONS
a(71)-a(87) from Amiram Eldar, Feb 19 2020
STATUS
approved