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

1,1

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)

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A266088 A122613 A115768 * A367348 A005015 A070069

Adjacent sequences: A242955 A242956 A242957 * A242959 A242960 A242961

Keyword

nonn,hard

Author

Felix Fröhlich, May 27 2014

Extensions

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

Status

approved