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%I A193929 #21 Sep 08 2022 08:45:58
%S A193929 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 A193929 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 A193929 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 A193929 Number of prime factors of n^4 + 1, counted with multiplicity.
%C A193929 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.
%H A193929 Amiram Eldar, <a href="/A193929/b193929.txt">Table of n, a(n) for n = 0..10000</a>
%F A193929 a(n) = A001222(A002523(n)) = bigomega(n^4+1) or Omega(n^4+1).
%e A193929 a(9) = 3 because 9^4+1 = 6562 = 2 * 17 * 193, which has 3 prime factors, counted with multiplicity
%t A193929 Join[{0}, Table[Total[Transpose[FactorInteger[n^4 + 1]][[2]]], {n, 100}]] (* _T. D. Noe_, Aug 10 2011 *)
%t A193929 Join[{0},Table[PrimeOmega[n^4+1],{n,120}]] (* _Harvey P. Dale_, Sep 25 2012 *)
%o A193929 (PARI) a(n) = bigomega(n^4+1); \\ _Michel Marcus_, Feb 09 2020
%o A193929 (Magma) [0] cat [&+[p[2]: p in Factorization(n^4+1)]:n in [1..120]]; // _Marius A. Burtea_, Feb 09 2020
%Y A193929 Cf. A001222, A002523, A193432, A193562.
%K A193929 nonn,easy
%O A193929 0,4
%A A193929 _Jonathan Vos Post_, Aug 09 2011

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