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Number of primes between factors of n-th semiprime.
6

%I #12 Apr 12 2021 04:42:07

%S 0,0,0,1,2,0,1,3,0,4,2,5,0,6,3,7,0,4,1,5,8,9,2,6,10,0,11,3,12,7,1,8,

%T 13,4,14,9,5,15,2,0,16,10,11,3,17,12,18,0,6,19,7,20,13,4,21,0,14,22,

%U 15,8,1,23,16,24,5,9,25,2,17,26,10,6,27,18,0,28,11,19,1,20,3,29,7,30

%N Number of primes between factors of n-th semiprime.

%C a(m)=0 iff m in A033476; a(m)>0 iff m in A089995.

%H Amiram Eldar, <a href="/A089994/b089994.txt">Table of n, a(n) for n = 1..10000</a>

%t pbfs[n_]:=Module[{f=PrimePi/@Transpose[FactorInteger[n]][[1]]}, Max[ 0,Last[f]-First[f]-1]]; pbfs/@Select[Range[300],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Apr 09 2012 *)

%Y Cf. A001358, A033476, A089995, A084126, A084127, A000720.

%K nonn

%O 1,5

%A _Reinhard Zumkeller_, Nov 19 2003