login
A247673
Least integer m > 0 with pi(m*n) = sigma(m) + sigma(n), where pi(.) and sigma(.) are given by A000720 and A000203 respectively.
7
23, 47, 359, 25, 11, 33, 9, 17, 182, 11, 15, 304, 12, 160, 6105, 444, 22676, 408, 5, 60, 8, 17888, 9, 125526, 1616818, 334976, 22584, 19548, 10, 286780, 21540, 6698792, 640720, 2466378, 75999272, 646104, 573678, 801525615, 1116040868, 3565308, 127408112
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..53 (terms a(5)-a(41) from Zhi-Wei Sun)
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
EXAMPLE
a(5) = 23 since pi(5*23) = 30 = sigma(5) + sigma(23).
MATHEMATICA
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}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 22 2014
EXTENSIONS
a(42)-a(45) from Hiroaki Yamanouchi, Oct 04 2014
STATUS
approved