A193330 Number of prime factors of n^2 + 1, counted with multiplicity.

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 2, 3, 1, 2, 1, 3, 3, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 2, 2, 3, 3, 3, 2, 2, 1, 3, 3, 2, 1, 3, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 3, 1, 3, 1, 5, 2, 2, 2, 2, 2, 3, 2, 2, 1, 3, 4, 2, 3, 2, 3, 4, 1, 3, 2, 3, 2, 2, 2, 3, 3, 4, 1, 2

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Jul 22 2011

Keywords

• nonn

Comments

a(n) is also the number of terms, counted with multiplicity, in a prime factorization of n + i in the ring of Gaussian integers. - Jason Kimberley, Dec 17 2011

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A046051, A054992, A193295.

Programs

Mathematica

A193330[n_Integer] := PrimeOmega[n^2 + 1];A193330 /@ Range[0, 100]
PrimeOmega/@(Range[0,90]^2+1) (* Harvey P. Dale, Apr 03 2019 *)

PARI

a(n)=bigomega(n^2+1) \\ Charles R Greathouse IV, Jul 23 2011