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Number of distinct prime-factors of ((prime(n)*(prime(n+1)-1)+(prime(n)-1)*prime(n+1))/2).
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%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