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.
%I A079142 #8 Oct 01 2013 17:57:33 %S A079142 4,6,8,9,12,15,25,30,35,49,56,63,121,132,143,169,182,195,289,306,323, %T A079142 361,380,399,529,552,575,841,870,899,961,992,1023,1369,1406,1443,1681, %U A079142 1722,1763,1849,1892,1935,2209,2256,2303,2809,2862,2915,3481,3540,3599 %N A079142 Numbers divisible by prime integer parts of their square roots. %C A079142 n is in the sequence if r=floor(sqrt(n)) is prime and r divides n. %C A079142 Union of the 3 sequences A001248={p^2}, A036690={p(p+1)} and {p(p+2)} for p prime. %C A079142 The sum of the reciprocals = 1.04... %F A079142 a(n) = prime(floor(n/3+1))*(prime(floor(n/3+1)) + (n mod 3)) %e A079142 56 is in the sequence because floor(sqrt(56)) = 7 is prime and 7 divides 56. %t A079142 Flatten[ #(#+{0, 1, 2})&/@Prime/@Range[20]] %t A079142 a[n_] := (p=Prime[Floor[n/3+1]])(p+Mod[n, 3]) %t A079142 dpipQ[n_]:=Module[{c=Floor[Sqrt[n]]},PrimeQ[c]&&Divisible[n,c]]; Select[Range[ 4000],dpipQ] (* _Harvey P. Dale_, Mar 10 2013 *) %o A079142 (PARI) ipsqrt(n) = { sr= 0; for(x=1,n, v = floor(sqrt(x)); if(isprime(v) && x%v == 0, print1(x" "); sr+=1.0/x; ); ); print(); print(sr); } \\ numbers divisible by prime integer parts of their square roots. %K A079142 nonn %O A079142 0,1 %A A079142 _Cino Hilliard_, Dec 26 2002