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A247602
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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.
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7
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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
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) exists for any n > 0.
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LINKS
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Table of n, a(n) for n=1..25.
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
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EXAMPLE
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a(1) = 3 since pi(1*3) = 2 = phi(1+3).
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = {my(m = 1); while (primepi(m*n) != eulerphi(m+n), m++); m; } \\ Michel Marcus, Sep 22 2014
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CROSSREFS
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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
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KEYWORD
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nonn,more
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AUTHOR
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Zhi-Wei Sun, Sep 21 2014
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EXTENSIONS
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a(21)-a(25) from Hiroaki Yamanouchi, Oct 04 2014
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STATUS
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approved
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