This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274175 #16 Jun 26 2016 13:38:19 %S A274175 133,1065,141373 %N A274175 Composite numbers c that set a new record for the number of bases b with 1 < b < c such that c satisfies b^(c-1) == 1 (mod c^2), i.e., such that c is a base-b "Wieferich pseudoprime". %C A274175 a(4) > 253263 if it exists. %C A274175 Is the sequence infinite? %C A274175 Let x be the integer sequence defined as x(n) = number of bases 1 < b < c such that c is a base-b "Wieferich pseudoprime", where c is the n-th composite number (that sequence does not have its own entry in the OEIS). Then a(n) is the sequence of composites where x(n) reaches record values. %C A274175 Let y be the integer sequence defined as y(n) = smallest composite c with exactly n bases 1 < b < c such that c is a base-b "Wieferich pseudoprime". Is a(n) = y(n) for all n? %C A274175 For every b with 1 < b < c such that c is a base-b "Wieferich pseudoprime", every prime factor p of c is a base-b Wieferich prime. %e A274175 c = 141373 satisfies b^(c-1) == 1 (mod c^2) for three values of b with 1 < b < c, namely b = 23382, 36620 and 130595. Since no other composite c < 141373 exists that has more than two such b, 141373 is a term of the sequence. %o A274175 (PARI) my(r=0, i); forcomposite(c=1, , i=0; for(b=2, c-1, if(Mod(b, c^2)^(c-1)==1, i++)); if(i > r, print1(c, ", "); r=i)) %Y A274175 Cf. A194946, A248865, A256517, A267288. %K A274175 nonn,hard,more,bref %O A274175 1,1 %A A274175 _Felix Fröhlich_, Jun 12 2016