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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
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
Sequence in context: A178055 A247856 A059660 * A339365 A035456 A035664
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.)