%I A117371
%S A117371 0,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,1,1,3,0,0,0,4,0,2,0,0,0,0,2,5,0,
%T A117371 0,0,6,3,1,0,1,0,3,0,7,0,0,0,1,4,4,0,0,1,2,5,8,0,0,0,9,1,0,2,2,0,5,6,1,
%U A117371 0,0,0,10,0,6,0,3,0,1,0,11,0,1,3,12,7,3,0,0,1,7,8,13,4,0,0,2,2,1,0,4,0
%N A117371 Number of primes between smallest prime divisor of n and largest prime 
               divisor of n which are coprime to n.
%C A117371 This sequence first differs from sequence A117370 at the 30th term.
%H A117371 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A117371 a(30) is 0 because the one prime (which is 3) between the smallest prime 
               dividing 30 (which is 2) and the largest prime dividing 30 (which 
               is 5) is not coprime to 30. On the other hand, a(14) = 2 because 
               there are two primes (3 and 5) which are between 14's least prime 
               divisor (2) and greatest prime divisor (7) and 3 and 5 are both coprime 
               to 14.
%p A117371 A020639 := proc(n) local ifs; if n = 1 then 1 ; else ifs := ifactors(n)[2] 
               ; min(seq(op(1,i),i=ifs)) ; fi ; end: A006530 := proc(n) local ifs; 
               if n = 1 then 1 ; else ifs := ifactors(n)[2] ; max(seq(op(1,i),i=ifs)) 
               ; fi ; end: A117371 := proc(n) local a,i ; a := 0 ; if n < 2 then 
               0 ; else for i from A020639(n)+1 to A006530(n)-1 do if isprime(i) 
               and gcd(i,n) = 1 then a := a+1 ; fi ; od; fi ; RETURN(a) ; end: seq(A117371(n),
               n=1..140) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 05 
               2007
%Y A117371 Cf. A117370.
%Y A117371 Sequence in context: A085858 A106671 A033776 this_sequence A117370 A151756 
               A112053
%Y A117371 Adjacent sequences: A117368 A117369 A117370 this_sequence A117372 A117373 
               A117374
%K A117371 nonn
%O A117371 1,14
%A A117371 Leroy Quet, Mar 10 2006
%E A117371 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 05 2007