A249909 Smallest prime factor of A241601(n), or 1 if A241601(n) = 1.

1, 1, 1, 1, 1, 1, 1, 61, 1, 277, 1, 19, 691, 43, 1, 47, 3617, 228135437, 43867, 79, 283, 41737, 131, 31, 103, 2137, 657931, 67, 9349, 71, 1721, 15669721, 37, 930157, 151628697551, 4153, 26315271553053477373, 9257, 154210205991661, 23489580527043108252017828576198947741, 137616929, 763601

Offset: 0

Author

Eric Chen, Dec 15 2014

Keywords

• nonn

Comments

Also the smallest prime factor of A246006(n) that is >= n+2.

a(n) = A020639(A241601(n)).

a(n) = 1 iff n is in the set {0, 1, 2, 3, 4, 5, 6, 8, 10, 14}.

a(189) is currently unknown; a(190)..a(199) = {5101, 559570609330768709, 40833790860803270336710504624737304862569304959957, 311, 467, 34110029, 461, 26034939865747697437451558982836040663625026070193, 34470847, 1879}.

All terms are Bernoulli or Euler irregular primes.

Links

• Eric Chen, Table of n, a(n) for n = 0..188
• Samuel Wagstaff, Factorization of Bernoulli and Euler numbers

Programs

Mathematica

a246006[n_] := If[EvenQ[n], Abs[Numerator[BernoulliB[n]]], Abs[EulerE[n-1]]];
a241601[n_] := a246006[n]/GCD[a246006[n], n!]
a = {}; Do[a = Append[a, FactorInteger[a241601[n]][[1, 1]]], {n, 0, 99} ]; a