A247672 Least integer m > 0 with pi(m*n) = phi(m) + phi(n), where pi(.) is the prime-counting function and phi(.) is Euler's totient function.

6, 2, 2, 23, 3, 1, 3, 1033, 2, 6449, 15887, 1, 100169, 268393, 636917, 2113589, 70324093, 1, 27852457, 78848479, 2, 468329417, 4, 1, 10220118551

Offset

1,1

Comments

Conjecture: a(n) exists for every 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 [math.NT], 2014-2017.

Example

a(1) = 6 since pi(6) = 3 = phi(1) + phi(6), and pi(1*m) = phi(1) + phi(m) for no m < 6.

Mathematica

Table[m = 1; While[PrimePi[n*m] != EulerPhi[m] + EulerPhi[n], m++]; m, {n, 1, 12}] (* Robert Price, Sep 08 2019 *)

Prog

(Perl) use ntheory ":all"; for my $n (1..16) { my $m=1; $m++ until (prime_count($m*$n) == euler_phi($m) + euler_phi($n)); say "$n $m"; } # Dana Jacobsen, Mar 07 2023

Crossrefs

Cf. A000010, A000720, A247600, A247601, A247602, A247603, A247604, A247673.

Sequence in context: A138995 A010133 A065280 * A188726 A272354 A353121

Adjacent sequences: A247669 A247670 A247671 * A247673 A247674 A247675

Keyword

nonn,more

Author

Zhi-Wei Sun, Sep 22 2014

Extensions

a(19)-a(25) from Hiroaki Yamanouchi, Oct 04 2014

Status

approved