A161889 -id:A161889 - cp's OEIS frontend

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

Mats Granvik, Jun 21 2009

nonn

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

Cf. A143104, A006590, A000005.

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 *)

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

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]

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

A161888 a(n) = the smallest positive integer that does not divide n, and is such that sum{k=1 to n} a(k) is coprime to n.

Original entry on oeis.org

2, 3, 2, 6, 3, 7, 2, 6, 4, 4, 2, 8, 2, 4, 4, 6, 2, 4, 2, 6, 4, 4, 2, 14, 3, 3, 4, 8, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 4, 6, 2, 4, 2, 6, 6, 4, 2, 10, 2, 4, 2, 6, 2, 4, 3, 3, 4, 4, 2, 8, 2, 4, 4, 6, 3, 5, 2, 6, 2, 8, 2, 10, 2, 4, 4, 6, 3, 9, 2, 6, 4, 4, 2, 8, 3, 3, 4, 6, 2, 4, 2, 6, 4, 4, 3, 5, 2, 4, 2, 8, 2, 8, 2, 6, 2

Offset: 1

Leroy Quet, Jun 21 2009

nonn

Sum{k=1 to n} a(k) = A161889(n).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A161889

spi[{n_,s_,a_}]:=Module[{k=1},While[Divisible[n+1,k]||!CoprimeQ[s+k, n+1], k++];{n+1,s+k,k}]; Transpose[NestList[spi,{1,2,2},105]][[3]] (* Harvey P. Dale, May 26 2015 *)

More terms from Sean A. Irvine, Aug 10 2010

cp's OEIS Frontend

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

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