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%I #30 Sep 08 2019 22:59:05
%S 2,1,13,31,73,181,443,2249,238839,6473,30001,40123,108539,251707,
%T 637321,7554079,4124437,241895689,27067097,69709723,179992919,
%U 1019958623,1208198863,3140421743,8179002173
%N Least positive integer m with pi(m*n) = phi(m), where pi(.) is the prime-counting function and phi(.) is Euler's totient function.
%C Conjecture: a(n) exists for any n > 0.
%C This is motivated by Golomb's result that for any n > 1 there is a positive integer m with mn/pi(mn) = n (i.e., pi(mn) = m).
%H S. W. Golomb, <a href="http://www.jstor.org/stable/2312732">On the Ratio of N to pi(N)</a>, American Mathematical Monthly, 69 (1962), 36-37.
%H 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 a(3) = 13 since pi(3*13) = 12 = phi(13).
%t Do[m=1;Label[aa];If[PrimePi[n*m]==EulerPhi[m],Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];
%t Label[bb];Continue,{n,1,18}]
%t Table[m = 1;
%t While[PrimePi[n*m] != EulerPhi[m], m++]; m, {n,1,12}] (* _Robert Price_, Sep 08 2019 *)
%Y Cf. A000010, A000720, A247600, A247602, A247603, A247604, A247672, A247673.
%K nonn,more
%O 1,1
%A _Zhi-Wei Sun_, Sep 21 2014
%E a(19)-a(25) from _Hiroaki Yamanouchi_, Oct 04 2014