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%I #34 Oct 28 2021 10:01:07
%S 0,1,1,1,0,0,1,1,1,2,1,1,1,1,0,1,2,1,0,0,1,1,1,1,1,1,1,0,1,1,1,1,1,2,
%T 2,3,1,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,0,1,0,1,1,
%U 1,1,1,1,1,2,1,1,0,2,1,1,1,1,1,1,1,1,1
%N Table T(b, m) of largest exponents k such that for p = prime(m) and base b > 1 the congruence b^(p-1) == 1 (mod p^k) is satisfied, or 0 if no such k exists, read by antidiagonals (downwards).
%C a(n) > 1 if b appears in row k, column n of the table in A257833 for k > 1 and n > 1.
%F a(n, m) = T(m+1, n-m), n >=2, m = 1, 2, ..., n-1. - _Wolfdieter Lang_, Jun 29 2015
%e T(3, 5) = 2, because the largest Wieferich exponent of prime(5) = 11 in base 3 is 2.
%e Table starts
%e b=2: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=3: 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=4: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=5: 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=6: 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=7: 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=8: 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=9: 3, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=10: 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=11: 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=12: 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=13: 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=14: 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1 ...
%e b=15: 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=16: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e b=17: 4, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ...
%e b=18: 0, 0, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 ...
%e b=19: 1, 2, 1, 3, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2 ...
%e b=20: 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ...
%e ....
%e The triangle a(n ,m) begins:
%e m 1 2 3 4 5 6 7 8 9 10 11 ...
%e n
%e 2 0
%e 3 1 1
%e 4 1 0 0
%e 5 1 1 1 2
%e 6 1 1 1 1 0
%e 7 1 2 1 0 0 1
%e 8 1 1 1 1 1 1 0
%e 9 1 1 1 1 1 2 2 3
%e 10 1 1 1 1 1 0 1 0 0
%e 11 1 1 1 1 1 1 1 1 2 1
%e 12 1 1 1 1 1 1 1 1 0 1 0
%e ...
%o (PARI) for(b=2, 20, forprime(p=1, 70, k=0; while(Mod(b, p^k)^(p-1)==1, k++); if(k > 0, k--); print1(k, ", ")); print(""))
%Y Cf. A001220, A257833.
%K nonn,tabl
%O 2,10
%A _Felix Fröhlich_, May 26 2015
%E Edited by _Wolfdieter Lang_, Jun 29 2015
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