A242958 Numbers n such that 3^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.

11, 22, 44, 55, 110, 220, 440, 880, 1006003, 2012006, 4024012, 11066033, 22132066, 44264132, 55330165, 88528264, 110660330, 221320660, 442641320, 885282640, 1770565280, 56224501667, 112449003334, 224898006668, 393571511669, 449796013336, 618469518337, 787143023338

Offset: 1

Author

Felix Fröhlich, May 27 2014

Keywords

• nonn
• hard

Comments

a(21) > 10^9.

All listed composite terms are multiples of the two known primes in this sequence, 11 and 1006003, the only known base 3 Wieferich primes.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..78 (terms < 10^15)

Crossrefs

Cf. A014127, A077816, A242959, A242960, A000010.

Programs

Mathematica

Select[Range[1000], Mod[3^EulerPhi[#], #^2] == 1 &] (* Alonso del Arte, Jun 02 2014 *)

PARI

for(n=2, 10^9, if(Mod(3, n^2)^(eulerphi(n))==1, print1(n, ", ")))

Extensions

Terms a(21) and beyond from Giovanni Resta, Jan 27 2020