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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
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
Sequence in context: A111092 A140732 A025023 * A157921 A033224 A142178
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Dec 26 2014
STATUS
approved

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Last modified July 14 20:04 EDT 2024. Contains 374323 sequences. (Running on oeis4.)