

A097651


a(n) is the earliest number m such that n*pi(m)=phi(m).


0



2, 11, 37, 169, 917, 1087, 15407, 10379, 30451, 64591, 187063, 498419, 1304707, 3523969, 9558541, 26042629, 73134517, 189963073, 528839387, 1394194181, 3779851321, 10246935931, 27800769133, 75370121689
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OFFSET

1,1


COMMENTS

It seems that for each n, a(n) exists and the set An={mn*pi(m)=phi(m)} is finite, for example A1={2,3,4,8,10,14,20,90}(elements of A1 are terms of the sequence A037171), A2={11,13,27,39,63,122,124, 136,152,176,224,322,364,410,460,1086,1164,3432,3612},... . According to the definition, a(n) is the smallest element of An. For n<19, 3 doesn't divide a(n), is this true for all terms of the sequence?


LINKS

Table of n, a(n) for n=1..24.


FORMULA

a[n_]:=(For[m=1, n*PrimePi[m]!=EulerPhi[m], m++ ];m)


EXAMPLE

a(18)=189963073 because 18*pi(189963073)=phi(189963073) and for m<189963073 18*pi(m)!= phi(m).


MATHEMATICA

a[n_]:=(For[m=1, n*PrimePi[m]!=EulerPhi[m], m++ ]; m); Do[Print[a[n]], {n, 18}]


CROSSREFS

Cf. A037171.
Sequence in context: A289616 A038607 A079009 * A320540 A059673 A294152
Adjacent sequences: A097648 A097649 A097650 * A097652 A097653 A097654


KEYWORD

more,nonn


AUTHOR

Farideh Firoozbakht, Sep 07 2004


EXTENSIONS

a(14) corrected and a(19)a(24) from Donovan Johnson, May 03 2010


STATUS

approved



