A193929 Number of prime factors of n^4 + 1, counted with multiplicity.

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

Amiram Eldar, Table of n, a(n) for n = 0..10000

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

Cf. A001222, A002523, A193432, A193562.

Sequence in context: A353351 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