%I A143145
%S A143145 1,2,4,6,9,12,15,16,20,25,30,35,36,42,49,56,63,64,70,72,77,80,81,88,90,
%T A143145 99,100,110,121,132,143,144,156,169,182,195,196,208,210,221,224,225,238,
%U A143145 240,255,256,272,289,306,323,324,342,361,380,399,400,418,420,437,440
%N A143145 A positive integer n is included if there are no primes p where j < p 
               < k, where j is the largest divisor of n that is <= sqrt(n) and k 
               = the smallest divisor of n that is >= sqrt(n).
%C A143145 All squares s are included in this sequence, since there are no integers 
               at all between j and k because j = k, where j = the largest divisor 
               of s that is <= sqrt(s) and k the smallest divisor of s that is >
               = sqrt(s).
%C A143145 Also, all integers of the form m = j*(j+1) are included in the sequence, 
               because the two middle divisors are j and j+1 and there are no integers 
               between these divisors, obviously.
%C A143145 The number of terms less than or equal to 10^n, n=0..., is 1, 5, 27, 
               100, 388, 1536, ..., . - Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 
               31 2008
%H A143145 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A143145 The divisors of 35 are 1,5,7,35. The two middle divisors are 5 and 7. 
               Between 5 and 7 (and not including 5 and 7) there are no primes (since 
               the only integer between these divisors, 6, is composite). So 35 
               is included in the sequence.
%t A143145 fQ[n_] := If[ IntegerQ@ Sqrt@ n, True, Block[ {d = Divisors@ n}, len 
               = Length@ d; lst = Take[ PrimeQ@ Range[ d[[len/2]], d[[len/2 + 1]]], 
               {2, -2}]; lst == {} || Union[ lst][[ -1]] != True]]; Select[ Range@ 
               459, fQ@# &] - Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 31 2008
%Y A143145 Cf. A143143, A143144.
%Y A143145 Sequence in context: A128716 A025057 A030763 this_sequence A130664 A014011 
               A064424
%Y A143145 Adjacent sequences: A143142 A143143 A143144 this_sequence A143146 A143147 
               A143148
%K A143145 nonn
%O A143145 1,2
%A A143145 Leroy Quet Jul 27 2008
%E A143145 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 31 2008