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A249306 Denominators A027642(n) of Bernoulli numbers except for a(4*k+5)=2 instead of 1. 1
1, 2, 6, 1, 30, 2, 42, 1, 30, 2, 66, 1, 2730, 2, 6, 1, 510, 2, 798, 1, 330, 2, 138, 1, 2730, 2, 6, 1, 870, 2, 14322, 1, 510, 2, 6, 1, 1919190, 2, 6, 1, 13530, 2, 1806, 1, 690, 2, 282, 1, 46410, 2, 66, 1, 1590, 2, 798, 1, 870, 2, 354, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

There exist an infinity of 1's, 2's, 6's, 30's, 42's, 66's, ... .

Respective ranks:

   0,   3,    7,   11,   15,   19, ...

   1,   5,    9,   13,   17,   21, ...   (= A016813)

   2,  14,   26,   34,   38,   62, ...   (= A051222)

   4,   8,   68,   76,  124,  152, ...   (= A051226)

   6, 114,  186,  258,  354,  402, ...   (= A051228)

  10,  50,  170,  370,  470,  590, ...   (= A051230)

  12,  24, 1308, 1884, 2004, 2364, ...   (= A249134)

  etc.

Hence by antidiagonals a permutation of A001477(n).

First column: A248614(n).

a(n) is an alternative sequence for the denominators of the Bernoulli numbers.

First 36 terms of the corresponding clockwise spiral:

.

  330------2----138------1---2730------2

    |                                  |

    |                                  |

    1     42------1-----30------2      6

    |      |                    |      |

    |      |                    |      |

  798      2      1------2     66      1

    |      |             |      |      |

    |      |             |      |      |

    2     30------1------6      1    870

    |                           |      |

    |                           |      |

  510------1------6------2---2730      2

                                       |

                                       |

    1------6------2----510------1--14322

LINKS

Table of n, a(n) for n=0..59.

Index entries for sequences related to Bernoulli numbers

FORMULA

a(2n) = A002445(n), a(2n+1) = A000034(n+1).

MAPLE

Clausen := proc(n) local S, i;

S := numtheory[divisors](n); S := map(i->i+1, S);

S := select(isprime, S); mul(i, i=S) end:

A249306 := n -> `if`(n mod 4 = 3, 1, Clausen(n)):

seq(A249306(n), n=0..59); # Peter Luschny, Nov 10 2014

MATHEMATICA

a[n_] := Denominator[BernoulliB[n]]; a[n_ /; Mod[n, 4] == 1] = 2; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Oct 28 2014 *)

CROSSREFS

A variant of the Clausen numbers A141056, A160014. And of A176591.

Cf. A000034, A002445, A016813, A027642, A051222, A051226, A051228, A051230, A090126, A164020, A248614, A249134.

Sequence in context: A132181 A291646 A027642 * A117214 A185972 A182918

Adjacent sequences:  A249303 A249304 A249305 * A249307 A249308 A249309

KEYWORD

nonn

AUTHOR

Paul Curtz, Oct 28 2014

STATUS

approved

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Last modified December 13 22:07 EST 2018. Contains 318087 sequences. (Running on oeis4.)