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 A193929 Number of prime factors of n^4 + 1, counted with multiplicity. 2

%I

%S 0,1,1,2,1,2,1,2,2,3,2,2,2,2,2,3,1,2,2,3,1,2,2,2,1,3,2,3,1,2,2,3,2,3,

%T 1,2,2,3,2,2,2,3,2,4,3,3,1,3,1,3,2,3,2,3,1,3,1,2,2,4,3,2,2,3,3,2,3,3,

%U 2,3,3,2,2,2,1,3,3,4,2,4,1,2,1,4,2,4,2,3,1,3,1,3,2,3,2,4,3,3,2,3,2,3,2,2,3,2,1,3,2,3,3,4,2,2,2,2,2,3,1

%N Number of prime factors of n^4 + 1, counted with multiplicity.

%C This is to A193330 as A002523(n) = n^4+1 is to A002522(n) = n^2 + 1. a(n) = 2 when n^4+1 is prime, iff n is in A037896.

%F a(n) = A001222(A002523(n)) = bigomega(n^4+1) or Omega(n^4+1).

%e a(9) = 3 because 9^4+1 = 6562 = 2 * 17 * 193, which has 3 prime factors, counted with multiplicity

%t Join[{0}, Table[Total[Transpose[FactorInteger[n^4 + 1]][[2]]], {n, 100}]] (* T. D. Noe, Aug 10 2011 *)

%t Join[{0},Table[PrimeOmega[n^4+1],{n,120}]] (* _Harvey P. Dale_, Sep 25 2012 *)

%Y Cf. A001222, A002523, A193432, A193562.

%K nonn,easy

%O 0,4

%A _Jonathan Vos Post_, Aug 09 2011

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