A247603 Least integer m > 0 with pi(m*n) = sigma(m), where sigma(m) is the sum of all positive divisors of m.

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}]

Crossrefs

Cf. A000203, A000720, A247600, A247601, A247602, A247604, A247672, A247673.

Sequence in context: A070934 A296272 A031915 * A102385 A290226 A214596

Adjacent sequences: A247600 A247601 A247602 * A247604 A247605 A247606

Keyword

nonn

Author

Zhi-Wei Sun, Sep 21 2014

Extensions

a(31)-a(42) from Hiroaki Yamanouchi, Oct 04 2014

Status

approved