

A273785


Numbers n where a composite c < n exists such that n^(c1) == 1 (mod c^2), i.e., such that c is a "basen 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
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

15 satisfies the congruence 26^(151) == 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 N1 do
if not isprime(c) then
for m in map(rhs@op, [msolve(x^(c1)1, c^2)]) do
if m > c and m <= N then Res:= Res union {m, seq(k*c^2+m, k=1..(Nm)/c^2)}
else Res:= Res union {seq(k*c^2+m, k=1..(Nm)/c^2)}
fi
od
fi
od:


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, n1, if(Mod(n, c^2)^(c1)==1, return(1))); return(0)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



