A241601 Largest divisor of A246006(n) whose prime factors are all >= n+2.

1, 1, 1, 1, 1, 1, 1, 61, 1, 277, 1, 50521, 691, 41581, 1, 199360981, 3617, 228135437, 43867, 2404879675441, 174611, 14814847529501, 77683, 69348874393137901, 236364091, 238685140977801337, 657931, 4087072509293123892361, 3392780147, 454540704683713199807

Offset

0,8

Comments

Notice: Not all a(n) are 1 or primes, the first example is a(11) = 50521, it equals 19*2659.

a(2n) is a product of powers of Bernoulli irregular primes (A000928), with the exception of n = 0,1,2,3,4,5,7.

a(2n+1) is a product of powers of Euler irregular primes (A120337), with the exception of n = 0,1,2.

Conjectures: All terms are squarefree, and there are infinitely many n such that a(n) is prime.

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

a(n) is prime for n = {7, 9, 12, 16, 17, 18, 26, 34, 36, 38, 39, 42, 49, 74, 114, 118, ...}.

All prime factors of a(n) are irregular primes (Bernoulli or Euler) and with an irregular pair to n: (61, 7), (277, 9), (19, 11), (2659, 11), (691, 12), (43, 13), (967, 13), (47, 15), (4241723, 15), (3617, 16), (228135437, 17), (43867, 18), (79, 19), (349, 19), (84224971, 19), ...

Number of ns such that a prime p divides a(n) is the irregular index of p, for example, 67 divides both a(27) and a(58), so it has irregular index two.

a(149) is the first a(n) which is not completely factored (with a 202-digit composite remaining).

Links

Table of n, a(n) for n=0..29.

Formula

a(2n) = |A001067(n)| = |A120082(2n)| = |A141590(n)| = |A060054(n)|.

a(2n+1) = A091912(n).

Mathematica

b[n_] := Numerator[BernoulliB[2 n]/(2 n)];
c[n_] := Numerator[SeriesCoefficient[Log[Tan[x]+1/Cos[x]], {x, 0, 2n+1}]];
a[0] = 1; a[n_] := If[EvenQ[n], b[n/2] // Abs, c[(n-1)/2]];
Table[a[n], {n, 0, 29}] (* _Jean-François Alcover_, Jul 03 2019 *)

Crossrefs

Cf. A246006.

Cf. A000928, A120337.

Cf. A001067, A120082, A141590, A060054, A091912.

Sequence in context: A058930 A333523 A249909 * A132096 A051322 A345224

Adjacent sequences: A241598 A241599 A241600 * A241602 A241603 A241604

Keyword

nonn

Author

_Eric Chen_, Dec 15 2014

Status

approved