OFFSET
1,2
COMMENTS
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).
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.
The number of terms less than or equal to 10^n, n=0..., is 1, 5, 27, 100, 388, 1536, ..., . - Robert G. Wilson v, Aug 31 2008
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MATHEMATICA
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, Aug 31 2008 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 27 2008
EXTENSIONS
More terms from Robert G. Wilson v, Aug 31 2008
STATUS
approved