cp's OEIS Frontend

A244752 Square array read by antidiagonals in which rows are indexed by composite numbers w and row w gives n such that n^(w-1) == 1 (mod w^2).

%I A244752 #32 Oct 28 2021 06:29:39
%S A244752 17,33,37,49,73,65,65,109,129,80,81,145,193,82,101,97,181,257,161,201,
%T A244752 145,113,217,321,163,301,289,197,129,253,385,242,401,433,393,26,145,
%U A244752 289,449,244,501,577,589,199,257,161,325,513,323,601,721,785,224,513
%N A244752 Square array read by antidiagonals in which rows are indexed by composite numbers w and row w gives n such that n^(w-1) == 1 (mod w^2).
%C A244752 We can say that "w is a Wieferich pseudoprime to base n".
%C A244752 Any prime factor of w is a Wieferich prime to base n.
%H A244752 Robert Price, <a href="/A244752/b244752.txt">Table of n, a(n) for n = 2..1276</a>
%e A244752 Table starts
%e A244752 w=4: 17, 33, 49, 65, 81, 97, 113, ....
%e A244752 w=6: 37, 73, 109, 145, 181, 217, ....
%e A244752 w=8: 65, 129, 193, 257, 321, 385, ....
%e A244752 w=9: 80, 82, 161, 163, 242, 244, ....
%e A244752 w=10: 101, 201, 301, 401, 501, 601, ....
%e A244752 w=12: 145, 289, 433, 577, 721, 865, ....
%e A244752 w=14: 197, 393, 589, 785, 981, ....
%e A244752 ....
%t A244752 T = {};
%t A244752 For[w = 4, w <= 100, w++,
%t A244752   If[PrimeQ[w], Continue[]];
%t A244752   t = {};
%t A244752   For [n = 2, n <= 10^5, n++,
%t A244752    If[Mod[n^(w - 1), w^2] == 1, AppendTo[t, n]]];
%t A244752   AppendTo[T, t]];
%t A244752 Print[TableForm[T]];
%t A244752 A244752 = {};
%t A244752 For[c = 1, c <= 50, c++,
%t A244752   For[r = 1, r <= c, r++, AppendTo[A244752, T[[r]][[c - r + 1]]]]];
%t A244752 A244752 (* _Robert Price_, Sep 07 2019 *)
%o A244752 (PARI) forcomposite(w=2, 20, print1("w=", w, ": "); for(n=2, 10^3, if(Mod(n, w^2)^(w-1)==1, print1(n, ", "))); print(""))
%Y A244752 Cf. A001220, A240719, A244249.
%K A244752 nonn,tabl
%O A244752 2,1
%A A244752 _Felix Fröhlich_, Jul 05 2014
%E A244752 a(17)-a(55) from _Robert Price_, Sep 07 2019