cp's OEIS Frontend

A237612 Least positive integer k such that A000720(k*n) is a square, or 0 if such a number k does not exist.

%I A237612 #12 Apr 06 2014 22:19:36
%S A237612 1,1,3,2,2,4,1,1,1,1,5,2,2,2,28,34,9,3,3,5,20,7,1,1,1,1,1,1,2,14,5,17,
%T A237612 3,16,12,23,18,4,4,30,46,10,50,23,36,18,40,14,2,2,3,3,1,1,1,1,1,1,32,
%U A237612 7,11,68,19,79,29,267,10,8,12,6
%N A237612 Least positive integer k such that A000720(k*n) is a square, or 0 if such a number k does not exist.
%C A237612 According to the conjecture in A237598, we should always have 0 < a(n) < prime(n).
%H A237612 Zhi-Wei Sun, <a href="/A237612/b237612.txt">Table of n, a(n) for n = 1..10000</a>
%H A237612 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A237612 a(3) = 3 since A000720(3*3) = 4 is a square, but neither A000720(1*3) = 2  nor A000720(2*3) = 3 is a square.
%t A237612 sq[n_]:=IntegerQ[Sqrt[PrimePi[n]]]
%t A237612 Do[Do[If[sq[k*n],Print[n," ",k];Goto[aa]],{k,1,Prime[n]-1}];
%t A237612 Print[n," ",0];Label[aa];Continue,{n,1,100}]
%Y A237612 Cf. A000290, A000720, A237578, A237597, A237598, A237614.
%K A237612 nonn
%O A237612 1,3
%A A237612 _Zhi-Wei Sun_, Feb 10 2014