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A242958 Numbers n such that 3^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function. 8
11, 22, 44, 55, 110, 220, 440, 880, 1006003, 2012006, 4024012, 11066033, 22132066, 44264132, 55330165, 88528264, 110660330, 221320660, 442641320, 885282640, 1770565280, 56224501667, 112449003334 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are no further terms up to 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

Table of n, a(n) for n=1..23.

MAPLE

with(numtheory): P:=proc(q) local n; for n from 1 to q do

if (3^phi(n) mod n^2)=1 then print(n); fi; od; end: P(10^10); # Paolo P. Lava, Jun 13 2014

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 * A005015 A070069 A178664

Adjacent sequences:  A242955 A242956 A242957 * A242959 A242960 A242961

KEYWORD

nonn,hard,more

AUTHOR

Felix Fröhlich, May 27 2014

EXTENSIONS

a(21)-a(23) from Giovanni Resta, Jun 06 2016

STATUS

approved

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Last modified October 23 04:16 EDT 2018. Contains 316519 sequences. (Running on oeis4.)