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A242958
Numbers n such that 3^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.
9
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
KEYWORD
nonn,hard
AUTHOR
Felix Fröhlich, May 27 2014
EXTENSIONS
Terms a(21) and beyond from Giovanni Resta, Jan 27 2020
STATUS
approved