login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343527 Number of ordered quadruples (w, x, y, z) with gcd(w, x, y, z) = 1 and 1 <= {w, x, y, z} <= 2^n. 7
1, 15, 239, 3823, 60735, 972191, 15517679, 248252879, 3969108895, 63506982943, 1015951568815, 16255093526239, 260068569617727, 4161109496115135, 66577084386669199, 1065232436999055375, 17043668344393625999, 272698739815301095247, 4363176901343767529551, 69810828455823683068415, 1116973047989955380768527 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..52 (n = 0..31 from Karl-Heinz Hofmann)

FORMULA

Lim_{n->infinity} a(n)/2^(4*n) = 1/zeta(4) = A215267 = 90/Pi^4.

a(n) = A082540(2^n).

EXAMPLE

.

For n=3, the size of the gris is 8 X 8 X 8 X 8:

.

              o------------x(w=8)-------------o

             /|.                            ./ |

            / |.                           ./  |

           /  |.                          ./   |

          /   |.                         ./    |

         /    |.                      z(w=8)   |

        /     |.                      . /      |

       /      |.                     . /       |

      /       |.                   .  /     y(w=8)

     o------------------------------.o         |

    |\        /|¯¯¯¯¯¯x(w=1)¯¯¯¯¯¯/. |         |

    | w      / |                 /.| |         |

    |  \ z(w=1)|                /. | |         |

    |   \  /   |y(w=1)         /.  | |         |

    |    \/-------------------/.   | |         |

    |     |                   |    | |         |        w | sums

    |     |  Cube at w = 1    |    | |         |      ----+-----

    |     |    8 X 8 X 8      | _ _| |---------o        1 |  512

    |     |    contains       |    / |         /        2 |  448

    |     |       512         |   /  |        /         3 |  504

    |     |    completely     |  /   |       /          4 |  448

    |     | reduced fractions | /    |      /           5 |  511

    |     |                   |/     |     /            6 |  441

    |     /------------------- \     |    /             7 |  511

    |    /                      \    |   /              8 |  448

    |   w                        w   |  /             ----+-----

    |  /                          \  | /     sum for a(3) | 3823

    | /                            \ |/

    o -------------------------------o

PROG

(Python)

from labmath import mobius

def A343527(n): return sum(mobius(k)*(2**n//k)**4 for k in range(1, 2**n+1))

CROSSREFS

Cf. A018805, A342632, A342586, A071778.

Cf. A342935, A342841, A082540, A343193.

Sequence in context: A093745 A071811 A157456 * A097262 A158557 A220821

Adjacent sequences:  A343524 A343525 A343526 * A343528 A343529 A343530

KEYWORD

nonn

AUTHOR

Karl-Heinz Hofmann, Apr 18 2021

EXTENSIONS

Edited by N. J. A. Sloane, Jun 13 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 16:45 EDT 2021. Contains 347487 sequences. (Running on oeis4.)