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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A346743 A087041 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

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Last modified May 19 05:04 EDT 2022. Contains 353826 sequences. (Running on oeis4.)