cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A157938 #7 Nov 21 2013 12:49:34
%S A157938 10,20,28,42,55,66,88,99,110,130,156,170,187,204,238,255,272,304,342,
%T A157938 368,391,414,460,483,506,551,580,609,638,696,725,754,783,812,868,930,
%U A157938 962,999,1036,1073,1110,1184,1221,1258,1295,1332,1394,1435,1476,1558
%N A157938 Numbers n divisible by the least prime >= sqrt(n) but not by the largest prime <= sqrt(n).
%C A157938 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.
%H A157938 Harvey P. Dale, <a href="/A157938/b157938.txt">Table of n, a(n) for n = 1..1000</a>
%F A157938 A157938 = A157936 \ A157942 = A157937 \ A006094, where A157937 = A157936 \ A001248.
%e A157938 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).
%e A157938 5,7,8 are not in this sequence, since not a multiple of 3=nextprime(sqrt(5))=nextprime(sqrt(8)).
%t A157938 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 *)
%o A157938 (PARI) for( n=5,1999, n % nextprime(sqrtint(n-1)+1) & next; n % precprime(sqrtint(n)) & print1(n","))
%Y A157938 Cf. A157940.
%K A157938 nonn
%O A157938 1,1
%A A157938 _M. F. Hasler_, Mar 10 2009