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.

A079142 Numbers divisible by prime integer parts of their square roots.

This page as a plain text file.
%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