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A253016 Numbers n such that 11^phi(n) == 1 (mod n^2), where phi(n) = A000010(n). 3
71, 142, 284, 355, 497, 710, 994, 1420, 1491, 1988, 2485, 2840, 2982, 3976, 4970, 5680, 5964, 7455, 9940, 11928, 14910, 19880, 23856, 29820, 39760, 59640, 79520, 119280, 238560, 477120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No further terms up to 10^9.

No more terms less than 10^10. - Robert G. Wilson v, Jan 18 2015

The first 30 terms are divisible by 71. Are there any terms not divisible by 71? - Robert Israel, Dec 30 2014

By Corollary 5.9 in Agoh, Dilcher, Skula (1997), if there are no further Wieferich primes to base 11 apart from 71, then the answer is no. - Felix Fröhlich, Dec 30 2014

LINKS

Table of n, a(n) for n=1..30.

T. Agoh, K. Dilcher and L. Skula, Fermat Quotients for Composite Moduli, J. Num. Theory, Vol. 66, Issue 1 (1997), 29-50.

MAPLE

select(t -> 11 &^ numtheory:-phi(t) mod t^2 = 1, [$1..10^6]); # Robert Israel, Dec 30 2014

MATHEMATICA

a253016[n_] := Select[Range[n], PowerMod[11, EulerPhi[#], #^2] == 1 &]; a253016[500000] (* Michael De Vlieger, Dec 29 2014; modified by Robert G. Wilson v, Jan 18 2015 *)

PROG

(PARI) for(n=2, 1e9, if(Mod(11, n^2)^(eulerphi(n))==1, print1(n, ", ")))

CROSSREFS

Cf. A077816, A242958, A242959, A242960, A245529, A241977, A241978.

Sequence in context: A111092 A140732 A025023 * A157921 A033224 A142178

Adjacent sequences:  A253013 A253014 A253015 * A253017 A253018 A253019

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Dec 26 2014

STATUS

approved

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Last modified September 18 23:16 EDT 2021. Contains 347548 sequences. (Running on oeis4.)