A247603 - OEIS

%I #21 Oct 05 2014 04:01:43

%S 1,2,23,61,8,22,16,12,202,386,30,36,174,10745,1684,2804,1616,40006,

%T 6764,996,5775,8131355,19974,11264,4446,27882,4848,32466,162712,

%U 532313373,2341816,30864,14544,63696,2880,390990,135200,133992,1331840,11621646,117990

%N Least integer m > 0 with pi(m*n) = sigma(m), where sigma(m) is the sum of all positive divisors of m.

%C Conjecture: a(n) exists for any n > 1.

%H Hiroaki Yamanouchi, <a href="/A247603/b247603.txt">Table of n, a(n) for n = 2..53</a>

%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) = 2 since pi(3*2) = 3 = sigma(2), and pi(3*1) = 2 > sigma(1) = 1.

%t Do[m=1;Label[aa];If[PrimePi[n*m]==DivisorSigma[1,m],Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];

%t Label[bb];Continue,{n,2,30}]

%Y Cf. A000203, A000720, A247600, A247601, A247602, A247604, A247672, A247673.

%K nonn

%O 2,2

%A _Zhi-Wei Sun_, Sep 21 2014

%E a(31)-a(42) from _Hiroaki Yamanouchi_, Oct 04 2014