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A161886 Number of nonzero elements in the n X n Redheffer matrix. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A198271 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

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Last modified September 26 08:07 EDT 2022. Contains 356987 sequences. (Running on oeis4.)