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

5,1

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..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.

Example

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

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}]

Crossrefs

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

Sequence in context: A244093 A195926 A195929 * A194659 A194186 A033668

Adjacent sequences: A247601 A247602 A247603 * A247605 A247606 A247607

Keyword

nonn

Author

Zhi-Wei Sun, Sep 21 2014

Extensions

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

Status

approved