%I #11 May 16 2017 04:30:26
%S 1,1,2,1,2,2,2,1,2,3,2,1,3,1,2,1,2,2,2,3,2,2,4,3,1,2,2,3,3,2,2,3,2,1,
%T 2,3,3,3,2,3,3,1,2,3,3,3,3,3,3,2,2,2,3,2,1,2,3,4,1,2,2,2,2,3,2,2,2,2,
%U 3,2,4,4,2,2,2,3,2,3,1,1,3,1,4,3,1,4,3,1,2,3,3,3,3,3,3,3,2,2,3,1,1,3,1,3,3
%N Number of distinct prime-factors of ((prime(n)*(prime(n+1)-1)+(prime(n)-1)*prime(n+1))/2).
%C a(n) = A001221(A099909(n)).
%H G. C. Greubel, <a href="/A099910/b099910.txt">Table of n, a(n) for n = 2..5000</a>
%t dpf[{a_,b_}]:=PrimeNu[((a(b-1))+(a-1)b)/2]; dpf/@Partition[Prime[ Range[ 2,110]],2,1] (* _Harvey P. Dale_, Nov 16 2011 *)
%o (PARI) a(n)=omega(((prime(n)*(prime(n+1)-1)+(prime(n)-1)*prime(n+1))/2)) \\ _Michel Marcus_, May 16 2017
%Y Cf. A099911, A098142 (a(n) is 1).
%K nonn
%O 2,3
%A _Reinhard Zumkeller_, Oct 29 2004