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A193929 Number of prime factors of n^4 + 1, counted with multiplicity. 2
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 (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. a(n) = 2 when n^4+1 is prime, iff n is in A037896.

LINKS

Table of n, a(n) for n=0..118.

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 *)

CROSSREFS

Cf. A001222, A002523, A193432, A193562.

Sequence in context: A324810 A178771 A289498 * A132881 A224702 A267263

Adjacent sequences:  A193926 A193927 A193928 * A193930 A193931 A193932

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Aug 09 2011

STATUS

approved

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)