A247602 Least positive integer m with pi(m*n) = phi(m+n), where pi(.) is the prime-counting function and phi(.) is Euler's totient function.

3, 2, 1, 91, 6, 5, 1, 5, 1, 8041, 15870, 39865, 1, 251625, 637064, 1829661, 4124240, 10553093, 1, 69709253, 179992156, 465769749, 1210576800, 3140421235, 13974959892

Offset

1,1

Comments

Conjecture: a(n) exists for any n > 0.

Links

Table of n, a(n) for n=1..25.

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

Example

a(1) = 3 since pi(1*3) = 2 = phi(1+3).

Mathematica

Do[m=1; Label[aa]; If[PrimePi[n*m]==EulerPhi[m+n], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa];
Label[bb]; Continue, {n, 1, 20}]
Table[m = 1;
While[PrimePi[n*m] != EulerPhi[m + n], m++]; m, {n, 1, 13}] (* Robert Price, Sep 08 2019 *)

Prog

(PARI) a(n) = {my(m = 1); while (primepi(m*n) != eulerphi(m+n), m++); m; } \\ Michel Marcus, Sep 22 2014

Crossrefs

Cf. A000010, A000720, A247600, A247601, A247603, A247604, A247672, A247673.

Sequence in context: A087041 A357675 A152790 * A201902 A239893 A178609

Adjacent sequences: A247599 A247600 A247601 * A247603 A247604 A247605

Keyword

nonn,more

Author

Zhi-Wei Sun, Sep 21 2014

Extensions

a(21)-a(25) from Hiroaki Yamanouchi, Oct 04 2014

Status

approved