

A247672


Least integer m > 0 with pi(m*n) = phi(m) + phi(n), where pi(.) is the primecounting 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
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..25.
ZhiWei Sun, A new theorem on the primecounting function, arXiv:1409.5685, 2014.


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

Do[m=1; Label[aa]; If[PrimePi[m*n]==EulerPhi[m]+EulerPhi[n], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 18}]
Table[m = 1;
While[PrimePi[n*m] != EulerPhi[m] + EulerPhi[n], m++]; m, {n, 1,
12}] (* Robert Price, Sep 08 2019 *)


CROSSREFS

Cf. A000010, A000720, A247600, A247601, A247602, A247603, A247604, A247673.
Sequence in context: A138995 A010133 A065280 * A188726 A272354 A196552
Adjacent sequences: A247669 A247670 A247671 * A247673 A247674 A247675


KEYWORD

nonn,more


AUTHOR

ZhiWei Sun, Sep 22 2014


EXTENSIONS

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


STATUS

approved



