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 A194003 Number of prime factors of n^8 + 1, counted with multiplicity. 2
 0, 1, 1, 3, 1, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 4, 3, 3, 2, 6, 2, 4, 3, 3, 2, 2, 2, 4, 3, 3, 2, 4, 6, 3, 2, 2, 4, 3, 3, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 5, 2, 3, 2, 4, 4, 4, 3, 6, 2, 5, 2, 2, 2, 5, 2, 5, 4, 4, 3, 4, 3, 5, 4, 2, 3, 4, 2, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is to A193330 as A002523(n) = n^4+1 is to A002522(n) = n^2 + 1, and as A060890(n) = n^8+1 is to A002522(n) = n^2 + 1. a(n) = 1 when n^8+1 is prime, iff n is in {1, 2, 4} unless there is a larger Fermat prime than 65537. LINKS Amiram Eldar, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A001222(A060890(n)) = bigomega(n^8+1) or Omega(n^8+1) EXAMPLE a(10) = 2 because 10^8 + 1 = 100000001 = 17 * 5882353 has 2 prime factors. a(40) = 6 because 40^8 + 1 = 6553600000001 = 17^2 * 113 * 337 * 641 * 929 has 6 prime factors (with multiplicity) and is the smallest example not squarefree. MATHEMATICA Join[{0}, Table[Total[Transpose[FactorInteger[n^8 + 1]][[2]]], {n, 50}]] PrimeOmega[Range[0, 90]^8+1] (* Harvey P. Dale, May 27 2018 *) PROG (PARI) a(n) = bigomega(n^8+1); \\ Michel Marcus, Feb 09 2020 (Magma) [0] cat [&+[p[2]: p in Factorization(n^8+1)]:n in [1..90]]; // Marius A. Burtea, Feb 09 2020 CROSSREFS Cf. A001222, A060890, A002523, A193432, A193562, A193929. Sequence in context: A178055 A247856 A059660 * A339365 A035456 A035664 Adjacent sequences: A194000 A194001 A194002 * A194004 A194005 A194006 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Aug 10 2011 STATUS approved

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Last modified May 23 14:49 EDT 2024. Contains 372763 sequences. (Running on oeis4.)