A157938 Numbers n divisible by the least prime >= sqrt(n) but not by the largest prime <= sqrt(n).

10, 20, 28, 42, 55, 66, 88, 99, 110, 130, 156, 170, 187, 204, 238, 255, 272, 304, 342, 368, 391, 414, 460, 483, 506, 551, 580, 609, 638, 696, 725, 754, 783, 812, 868, 930, 962, 999, 1036, 1073, 1110, 1184, 1221, 1258, 1295, 1332, 1394, 1435, 1476, 1558

Offset: 1

Author

M. F. Hasler, Mar 10 2009

Keywords

• nonn

Comments

Also: Numbers n divisible by the least prime >= sqrt(n) which are not in A001248 (primes squared) or A006094 (product of two consecutive primes). A subsequence of A157937.

Examples

			a(1)=10 and a(2)=20 are divisible by 5 = nextprime(sqrt(10)) = nextprime(sqrt(20)) and neither a prime squared (as are 4 and 9) nor product of consecutive primes (as are 6 and 15).
5,7,8 are not in this sequence, since not a multiple of 3=nextprime(sqrt(5))=nextprime(sqrt(8)).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A157940.

Programs

Mathematica

dpQ[n_]:=Module[{srn=Sqrt[n],a,b},a=If[PrimeQ[srn],srn,NextPrime[ srn]];b=If[PrimeQ[srn],srn,NextPrime[srn,-1]]; Divisible[n,a]&& !Divisible[ n,b]]; Select[Range[2000],dpQ] (* Harvey P. Dale, Oct 10 2011 *)

PARI

for( n=5,1999, n % nextprime(sqrtint(n-1)+1) & next; n % precprime(sqrtint(n)) & print1(n","))

Formula

A157938 = A157936 \ A157942 = A157937 \ A006094, where A157937 = A157936 \ A001248.