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%I #21 Oct 05 2014 04:00:55
%S 23,47,359,25,11,33,9,17,182,11,15,304,12,160,6105,444,22676,408,5,60,
%T 8,17888,9,125526,1616818,334976,22584,19548,10,286780,21540,6698792,
%U 640720,2466378,75999272,646104,573678,801525615,1116040868,3565308,127408112
%N Least integer m > 0 with pi(m*n) = sigma(m) + sigma(n), where pi(.) and sigma(.) are given by A000720 and A000203 respectively.
%C Conjecture: a(n) exists for every n = 5, 6, ... .
%H Zhi-Wei Sun and Hiroaki Yamanouchi, <a href="/A247673/b247673.txt">Table of n, a(n) for n = 5..53</a> (terms a(5)-a(41) 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) = 23 since pi(5*23) = 30 = sigma(5) + sigma(23).
%t Do[m=1; Label[aa]; If[PrimePi[m*n]==DivisorSigma[1,m]+DivisorSigma[1,n], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 5, 41}]
%Y Cf. A000203, A000720, A247600, A247601, A247602, A247603, A247604, A247672.
%K nonn
%O 5,1
%A _Zhi-Wei Sun_, Sep 22 2014
%E a(42)-a(45) from _Hiroaki Yamanouchi_, Oct 04 2014