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 A082863 #28 Aug 06 2014 03:25:53
%S A082863 1,1,2,2,2,2,2,2,2,3,2,3,3,2,3,2,2,3,3,3,3,3,2,3,2,3,2,4,2,3,3,2,4,3,
%T A082863 3,3,3,3,3,4,2,4,3,3,3,3,2,3,3,3,3,3,3,3,4,3,3,4,2,4,3,2,4,3,3,4,3,4,
%U A082863 3,4,2,3,3,3,4,4,3,4,2,3,2,4,3,4,4,3,3,4,3,4,4,3,4,3,3,3,3,3,3
%N A082863 Number of distinct prime factors of n^2-1.
%C A082863 This is a very slowly growing sequence - by n=100000 the maximum value is 8.
%C A082863 If n is in A014574 then a(n) = 2. - _Robert Israel_, Aug 05 2014
%H A082863 T. D. Noe, <a href="/A082863/b082863.txt">Table of n, a(n) for n = 2..10000</a>
%F A082863 a(n) = A001221((n-1)*(n+1)).
%F A082863 a(n) = A001221(n-1) + A001221(n+1) + ((-1)^n - 1)/2. - _Robert Israel_, Aug 05 2014
%e A082863 a(11)=3 because (11-1)*(11+1)=10*12=2^3*3*5, which has 3 distinct prime factors, namely 2,3 and 5.
%p A082863 A082863 := proc(n)
%p A082863 A001221(n^2-1) ;
%p A082863 end proc: # _R. J. Mathar_, Aug 05 2014
%p A082863 # alternative:
%p A082863 A082863:= n -> nops(numtheory:-factorset(n^2-1)):
%p A082863 seq(A082863(n), n=1..100); # _Robert Israel_, Aug 05 2014
%t A082863 Table[PrimeNu[n^2-1],{n,2,100}] (* _Harvey P. Dale_, Jul 05 2011 *)
%o A082863 (PARI) for (n=2,100,print1(omega((n-1)*(n+1))","))
%Y A082863 Cf. A001221, A014574, A219017 (greedy inverse).
%K A082863 nonn
%O A082863 2,3
%A A082863 _Jon Perry_, May 24 2003