cp's OEIS Frontend

A247602 Least positive integer m with pi(m*n) = phi(m+n), where pi(.) is the prime-counting function and phi(.) is Euler's totient function.

%I A247602 #29 Sep 08 2019 22:59:57
%S A247602 3,2,1,91,6,5,1,5,1,8041,15870,39865,1,251625,637064,1829661,4124240,
%T A247602 10553093,1,69709253,179992156,465769749,1210576800,3140421235,
%U A247602 13974959892
%N A247602 Least positive integer m with pi(m*n) = phi(m+n), where pi(.) is the prime-counting function and phi(.) is Euler's totient function.
%C A247602 Conjecture: a(n) exists for any n > 0.
%H A247602 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1409.5685">A new theorem on the prime-counting function</a>, arXiv:1409.5685, 2014.
%e A247602 a(1) = 3 since pi(1*3) = 2 = phi(1+3).
%t A247602 Do[m=1;Label[aa];If[PrimePi[n*m]==EulerPhi[m+n],Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];
%t A247602 Label[bb];Continue,{n,1,20}]
%t A247602 Table[m = 1;
%t A247602 While[PrimePi[n*m] != EulerPhi[m + n], m++]; m, {n, 1, 13}] (* _Robert Price_, Sep 08 2019 *)
%o A247602 (PARI) a(n) = {my(m = 1); while (primepi(m*n) != eulerphi(m+n), m++); m;} \\ _Michel Marcus_, Sep 22 2014
%Y A247602 Cf. A000010, A000720, A247600, A247601, A247603, A247604, A247672, A247673.
%K A247602 nonn,more
%O A247602 1,1
%A A247602 _Zhi-Wei Sun_, Sep 21 2014
%E A247602 a(21)-a(25) from _Hiroaki Yamanouchi_, Oct 04 2014