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A273785 Numbers n where a composite c < n exists such that n^(c-1) == 1 (mod c^2), i.e., such that c is a "base-n Wieferich pseudoprime". 2
17, 26, 33, 37, 49, 65, 73, 80, 81, 82, 97, 99, 101, 109, 113, 129, 145, 146, 161, 163, 168, 170, 177, 181, 182, 193, 197, 199, 201, 209, 217, 224, 225, 226, 239, 241, 242, 244, 251, 253, 257, 268, 273, 289, 293, 301, 305, 321, 323, 325, 337, 353, 360, 361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contains n+1 for n in A048111. - Robert Israel, Apr 20 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..5000

EXAMPLE

15 satisfies the congruence 26^(15-1) == 1 (mod 15^2) and 15 < 26, so 26 is a term of the sequence.

MAPLE

N:= 1000: # to get all terms <= N

Res:= {}:

for c from 4 to N-1 do

  if not isprime(c) then

    for m in map(rhs@op, [msolve(x^(c-1)-1, c^2)]) do

       if m > c and m <= N then Res:= Res union {m, seq(k*c^2+m, k=1..(N-m)/c^2)}

       else Res:= Res union {seq(k*c^2+m, k=1..(N-m)/c^2)}

       fi

    od

  fi

od:

sort(convert(Res, list)); # Robert Israel, Apr 20 2017

MATHEMATICA

nn = 361; c = Select[Range@ nn, CompositeQ]; Select[Range@ nn, Function[n, Count[TakeWhile[c, # <= n &], k_ /; Mod[n^(k - 1), k^2] == 1] > 0]] (* Michael De Vlieger, May 30 2016 *)

PROG

(PARI) is(n) = forcomposite(c=1, n-1, if(Mod(n, c^2)^(c-1)==1, return(1))); return(0)

CROSSREFS

Cf. A048111, A240719, A244752, A255885, A256517, A267288, A268310, A273339, A273340.

Sequence in context: A129910 A259075 A212909 * A171169 A316561 A034963

Adjacent sequences:  A273782 A273783 A273784 * A273786 A273787 A273788

KEYWORD

nonn

AUTHOR

Felix Fröhlich, May 30 2016

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)