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

0,4

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

Mathematica

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

Prog

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

Crossrefs

Cf. A046051, A054992, A193295.

Sequence in context: A204893 A251717 A057217 * A147810 A305302 A340382

Adjacent sequences: A193327 A193328 A193329 * A193331 A193332 A193333

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 22 2011

Status

approved