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A247603
Least integer m > 0 with pi(m*n) = sigma(m), where sigma(m) is the sum of all positive divisors of m.
8
1, 2, 23, 61, 8, 22, 16, 12, 202, 386, 30, 36, 174, 10745, 1684, 2804, 1616, 40006, 6764, 996, 5775, 8131355, 19974, 11264, 4446, 27882, 4848, 32466, 162712, 532313373, 2341816, 30864, 14544, 63696, 2880, 390990, 135200, 133992, 1331840, 11621646, 117990
OFFSET
2,2
COMMENTS
Conjecture: a(n) exists for any n > 1.
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 2..53
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
EXAMPLE
a(3) = 2 since pi(3*2) = 3 = sigma(2), and pi(3*1) = 2 > sigma(1) = 1.
MATHEMATICA
Do[m=1; Label[aa]; If[PrimePi[n*m]==DivisorSigma[1, m], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa];
Label[bb]; Continue, {n, 2, 30}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 21 2014
EXTENSIONS
a(31)-a(42) from Hiroaki Yamanouchi, Oct 04 2014
STATUS
approved