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A193929
Number of prime factors of n^4 + 1, counted with multiplicity.
3
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, 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, 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
OFFSET
0,4
COMMENTS
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.
LINKS
FORMULA
a(n) = A001222(A002523(n)) = bigomega(n^4+1) or Omega(n^4+1).
EXAMPLE
a(9) = 3 because 9^4+1 = 6562 = 2 * 17 * 193, which has 3 prime factors, counted with multiplicity
MATHEMATICA
Join[{0}, Table[Total[Transpose[FactorInteger[n^4 + 1]][[2]]], {n, 100}]] (* T. D. Noe, Aug 10 2011 *)
Join[{0}, Table[PrimeOmega[n^4+1], {n, 120}]] (* Harvey P. Dale, Sep 25 2012 *)
PROG
(PARI) a(n) = bigomega(n^4+1); \\ Michel Marcus, Feb 09 2020
(Magma) [0] cat [&+[p[2]: p in Factorization(n^4+1)]:n in [1..120]]; // Marius A. Burtea, Feb 09 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Aug 09 2011
STATUS
approved