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Least integer m > 0 with pi(m*n) = sigma(m+n), where pi(.) and sigma(.) are given by A000720 and A000203.
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%I #25 Oct 05 2014 04:01:51

%S 18,11,360,251,168,36,6,285,1185,792,29,11,245078,5,1869,46074,573,

%T 42863,11,5,8129,60806,1443,452,15,39298437,386891,1041920,1290489,

%U 17630,35569,10,8174777,3152500,4291325,57880072,55991485,127358,93462807,93314912

%N Least integer m > 0 with pi(m*n) = sigma(m+n), where pi(.) and sigma(.) are given by A000720 and A000203.

%C Conjecture: a(n) exists for every n = 5,6,...

%H Zhi-Wei Sun and Hiroaki Yamanouchi, <a href="/A247604/b247604.txt">Table of n, a(n) for n = 5..52</a> (terms a(5)-a(40) from Zhi-Wei Sun)

%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(5) = 18 since pi(5*18) = 24 = sigma(5+18).

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

%t Label[bb];Continue,{n,5,40}]

%Y Cf. A000203, A000720, A247600, A247601, A247602, A247603, A247672, A247673.

%K nonn

%O 5,1

%A _Zhi-Wei Sun_, Sep 21 2014

%E a(41)-a(44) from _Hiroaki Yamanouchi_, Oct 04 2014