A247604 Least integer m > 0 with pi(m*n) = sigma(m+n), where pi(.) and sigma(.) are given by A000720 and A000203.

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

Author

Zhi-Wei Sun, Sep 21 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for every n = 5,6,...

Examples

			a(5) = 18 since pi(5*18) = 24 = sigma(5+18).
		

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.

Crossrefs

Cf. A000203, A000720, A247600, A247601, A247602, A247603, A247672, A247673.

Programs

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}]

Extensions

a(41)-a(44) from Hiroaki Yamanouchi, Oct 04 2014