A097651 a(n) is the earliest number m such that n*pi(m)=phi(m).

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

Offset

1,1

Comments

It seems that for each n, a(n) exists and the set An={m|n*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.

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}]

Prog

(PARI) a(n) = my(m=1); while (n*primepi(m) != eulerphi(m), m++); m; \\ Michel Marcus, Oct 31 2025

Crossrefs

Cf. A000010, A000720, A037171.

Sequence in context: A289616 A038607 A079009 * A320540 A059673 A294152

Adjacent sequences: A097648 A097649 A097650 * A097652 A097653 A097654

Keyword

nonn,more

Author

Farideh Firoozbakht, Sep 07 2004

Extensions

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

Status

approved