cp's OEIS Frontend

A237597 a(n) = |{0 < k < prime(n): n divides pi(k*n)}|, where pi(.) is given by A000720.

%I A237597 #10 Feb 10 2014 06:20:48
%S A237597 1,1,1,2,2,1,1,3,4,3,3,3,2,4,3,3,5,7,1,3,3,5,2,5,4,4,5,5,3,7,3,2,3,4,
%T A237597 8,4,2,6,4,5,6,8,7,2,8,2,7,1,3,6,4,6,5,1,7,4,4,3,5,6,4,8,6,5,2,5,8,4,
%U A237597 2,5,7,5,3,1,3,2,6,3,2,4
%N A237597 a(n) = |{0 < k < prime(n): n divides pi(k*n)}|, where pi(.) is given by A000720.
%C A237597 Conjecture: a(n) > 0 for all n > 0.
%C A237597 See also A237614 for the least k > 0 with pi(k*n) divisible by n.
%H A237597 Zhi-Wei Sun, <a href="/A237597/b237597.txt">Table of n, a(n) for n = 1..2500</a>
%e A237597 a(6) = 1 since pi(11*6) = 3*6 with 11 < prime(6) = 13.
%e A237597 a(19) = 1 since pi(33*19) = 6*19 with 33 < prime(19) = 67.
%e A237597 a(759) = 1 since pi(2559*759) = 191*759 with 2559 < prime(759) = 5783.
%t A237597 a[n_]:=Sum[If[Mod[PrimePi[k*n],n]==0,1,0],{k,1,Prime[n]-1}]
%t A237597 Table[a[n],{n,1,80}]
%Y A237597 Cf. A000040, A000720, A237578, A237598, A237612, A237614.
%K A237597 nonn
%O A237597 1,4
%A A237597 _Zhi-Wei Sun_, Feb 10 2014