This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A193330 #31 Jun 30 2025 15:31:01 %S A193330 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, %T A193330 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, %U A193330 4,2,3,2,3,4,1,3,2,3,2,2,2,3,3,4,1,2 %N A193330 Number of prime factors of n^2 + 1, counted with multiplicity. %C A193330 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 %H A193330 Charles R Greathouse IV, <a href="/A193330/b193330.txt">Table of n, a(n) for n = 0..10000</a> %t A193330 A193330[n_Integer] := PrimeOmega[n^2 + 1];A193330 /@ Range[0, 100] %t A193330 PrimeOmega/@(Range[0,90]^2+1) (* _Harvey P. Dale_, Apr 03 2019 *) %o A193330 (PARI) a(n)=bigomega(n^2+1) \\ _Charles R Greathouse IV_, Jul 23 2011 %Y A193330 Cf. A046051, A054992, A193295. %K A193330 nonn %O A193330 0,4 %A A193330 _Vladimir Joseph Stephan Orlovsky_, Jul 22 2011