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 A238165 #16 Feb 20 2014 06:43:15
%S A238165 0,1,1,2,3,2,1,5,5,5,3,5,12,5,5,7,3,2,12,7,8,9,9,6,6,11,9,12,9,15,12,
%T A238165 12,13,7,16,12,18,15,16,11,8,8,13,15,20,13,7,15,13,7,18,7,18,15,11,15,
%U A238165 15,12,15,17,6,18,17,16,11,15,9,18,15,13
%N A238165 Number of pairs {j, k} with 0 < j < k <= n such that pi(j*n) divides pi(k*n), where pi(.) is given by A000720.
%C A238165 Conjecture: (i) a(n) > 0 for all n > 1.
%C A238165 (ii) For any integer n > 4, the sequence pi(k*n)^(1/k) (k = 1, ..., n) is strictly decreasing.
%C A238165 See also A238224 for a refinement of part (i) of this conjecture.
%H A238165 Zhi-Wei Sun, <a href="/A238165/b238165.txt">Table of n, a(n) for n = 1..400</a>
%e A238165 a(5) = 3 since pi(1*5) = 3 divides both pi(3*5) = 6 and pi(5*5) = 9, and pi(2*5) = 4 divides pi(4*5) = 8.
%e A238165 a(7) = 1 since pi(1*7) = 4 divides pi(3*7) = 8.
%t A238165 m[k_,j_]:=Mod[PrimePi[k],PrimePi[j]]==0
%t A238165 a[n_]:=Sum[If[m[k*n,j*n],1,0],{k,2,n},{j,1,k-1}]
%t A238165 Do[Print[n," ",a[n]],{n,1,70}]
%Y A238165 Cf. A000720, A237578, A237597, A237598, A237612, A237614, A237615, A238224.
%K A238165 nonn
%O A238165 1,4
%A A238165 _Zhi-Wei Sun_, Feb 19 2014