A247673 Least integer m > 0 with pi(m*n) = sigma(m) + sigma(n), where pi(.) and sigma(.) are given by A000720 and A000203 respectively.

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}]

Crossrefs

Cf. A000203, A000720, A247600, A247601, A247602, A247603, A247604, A247672.

Sequence in context: A180945 A052229 A054203 * A216569 A042054 A084667

Adjacent sequences: A247670 A247671 A247672 * A247674 A247675 A247676

Keyword

nonn

Author

Zhi-Wei Sun, Sep 22 2014

Extensions

a(42)-a(45) from Hiroaki Yamanouchi, Oct 04 2014

Status

approved