A161886 Number of nonzero elements in the n X n Redheffer matrix.

1, 4, 7, 11, 14, 19, 22, 27, 31, 36, 39, 46, 49, 54, 59, 65, 68, 75, 78, 85, 90, 95, 98, 107, 111, 116, 121, 128, 131, 140, 143, 150, 155, 160, 165, 175, 178, 183, 188, 197, 200, 209, 212, 219, 226, 231, 234, 245, 249, 256, 261, 268, 271, 280, 285, 294, 299, 304

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Formula

a(n) = A006590(n)+A000005(n)-1. [Enrique Pérez Herrero, Sep 28 2009]

a(n) = A006218(n)+n-1. [Enrique Pérez Herrero, Sep 25 2009]

a(1) = 1, a(n) = a(n-1) + A000005(n) + 1 for n > 1. a(1) = 1, a(n) = A006218(n+1) - A000005(n+1) + n - 1 = A006218(n+1) + A049820(n+1) - 2 = A006590(n+1) - 2 for n > 1. [Jaroslav Krizek, Nov 08 2009]

Example

The 4x4 Redheffer matrix:
  1,1,1,1
  1,1,0,0
  1,0,1,0
  1,1,0,1
contains 11 nonzero elements.

Mathematica

A161886[n_] := Plus @@ Table[DivisorSigma[0, i], {i, 1, n}] + n - 1 (* Enrique Pérez Herrero, Sep 25 2009 *)
A161886[n_] := Total[Table[ Boole[Divisible[i, j] || (i == 1)], {i, 1, n}, {j, 1, n}], Infinity] (* Enrique Pérez Herrero, Sep 25 2009 *)
A161889[n_] := Plus @@ Plus @@ Table[Boole[Divisible[i, j] || (i == 1)], {i, 1, n}, {j, 1, n}] (* Enrique Pérez Herrero, Sep 28 2009 *)
A161889[n_] := Sum[Ceiling[n/i], {i, 1, n}] + DivisorSigma[0, n] - 1 (* Enrique Pérez Herrero, Sep 28 2009 *)

Prog

(Python)
from math import isqrt
def A161886(n): return (lambda m: 2*sum(n//k for k in range(1, m+1))+n-1-m*m)(isqrt(n)) # Chai Wah Wu, Oct 09 2021

Crossrefs

Cf. A143104, A006590, A000005.

Sequence in context: A368649 A310730 A310731 * A310732 A310733 A310734

Adjacent sequences: A161883 A161884 A161885 * A161887 A161888 A161889

Keyword

nonn

Author

Mats Granvik, Jun 21 2009

Extensions

Edited by N. J. A. Sloane, Jun 26 2009

Status

approved