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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
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
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
KEYWORD
nonn,more
AUTHOR
Zhi-Wei Sun, Sep 22 2014
EXTENSIONS
a(19)-a(25) from Hiroaki Yamanouchi, Oct 04 2014
STATUS
approved