A248614 Rank of the n-th distinct value of the Bernoulli denominators in the sequence of the denominators of the Bernoulli numbers.

0, 1, 2, 4, 6, 10, 12, 16, 18, 20, 22, 28, 30, 36, 40, 42, 44, 46, 48, 52, 58, 60, 66, 70, 72, 78, 80, 82, 84, 88, 90, 92, 96, 100, 102, 106, 108, 110, 112, 116, 120, 126, 130, 132, 136, 138, 140, 144, 148, 150, 156, 162, 164, 166, 172, 174, 176, 178, 180, 190, 192

Offset

0,3

Comments

Consider sequence A027642 of the denominators of the Bernoulli numbers and the reduced sequence b(n) = 1, 2, 6, 30, 42, 66,... if duplicates are removed (which is 1, 2 followed by A090126). a(n) shows the smallest index --place of first appearance-- of b(n) in the full list A027642.

If n is of the form A002322(p*q) with p*q semiprime, then n is a term. The number 3652 is a term, but it is not of the form A002322(p*q), as Carl Pomerance noted. - Thomas Ordowski, Apr 28 2021; in place of an incorrect comment by Filip Zaludek, Sep 23 2016

For n > 0, numbers n such that A002322(A027642(n)) = n. - Thomas Ordowski, Jul 11 2018

Carl Pomerance (in answer to my question) proved that the set of these numbers has asymptotic density zero. - Thomas Ordowski, Apr 28 2021

Links

Table of n, a(n) for n=0..60.

Example

b(2)=6 appears first in A027642(2), so a(2)=2. b(4)=42 appears first as A027642(6)=42, so a(4)=6. b(5)=66 appears first as A027642(10), so a(5)=10.

Mathematica

BB = Table[Denominator[BernoulliB[n]], {n, 2, 400, 2}]; For[t = BB; n = 1, n <= Length[t], n++, p = Position[t, t[[n]]] // Rest; t = Delete[t, p]]; reducedBB = Join[{1, 2}, t]; a[0] = 0; a[1] = 1; a[n_] := 2*Position[BB, reducedBB[[n+1]], 1, 1][[1, 1]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 16 2014 *)

Prog

(PARI) L=List(); N=60; forprime(p=2, N*N, forprime(q=p, N*N, listput(L, lcm(p-1, q-1)) )); listsort(L, 1); for (i=1, N, print1(L[i], ", ")) \\ Filip Zaludek, Sep 23 2016

Crossrefs

Cf. A002322, A002445, A027642, A090126, A090801, A317210.

Sequence in context: A232964 A348442 A132631 * A105965 A229489 A355643

Adjacent sequences: A248611 A248612 A248613 * A248615 A248616 A248617

Keyword

nonn

Author

Paul Curtz, Oct 09 2014

Status

approved