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A247604
Least integer m > 0 with pi(m*n) = sigma(m+n), where pi(.) and sigma(.) are given by A000720 and A000203.
8
18, 11, 360, 251, 168, 36, 6, 285, 1185, 792, 29, 11, 245078, 5, 1869, 46074, 573, 42863, 11, 5, 8129, 60806, 1443, 452, 15, 39298437, 386891, 1041920, 1290489, 17630, 35569, 10, 8174777, 3152500, 4291325, 57880072, 55991485, 127358, 93462807, 93314912
OFFSET
5,1
COMMENTS
Conjecture: a(n) exists for every n = 5,6,...
LINKS
Zhi-Wei Sun and Hiroaki Yamanouchi, Table of n, a(n) for n = 5..52 (terms a(5)-a(40) from Zhi-Wei Sun)
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
EXAMPLE
a(5) = 18 since pi(5*18) = 24 = sigma(5+18).
MATHEMATICA
Do[m=1; Label[aa]; If[PrimePi[n*m]==DivisorSigma[1, m+n], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa];
Label[bb]; Continue, {n, 5, 40}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 21 2014
EXTENSIONS
a(41)-a(44) from Hiroaki Yamanouchi, Oct 04 2014
STATUS
approved