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

%I A161886 #12 Oct 10 2021 06:11:36
%S A161886 1,4,7,11,14,19,22,27,31,36,39,46,49,54,59,65,68,75,78,85,90,95,98,
%T A161886 107,111,116,121,128,131,140,143,150,155,160,165,175,178,183,188,197,
%U A161886 200,209,212,219,226,231,234,245,249,256,261,268,271,280,285,294,299,304
%N A161886 Number of nonzero elements in the n X n Redheffer matrix.
%F A161886 a(n) = A006590(n)+A000005(n)-1. [_Enrique Pérez Herrero_, Sep 28 2009]
%F A161886 a(n) = A006218(n)+n-1. [_Enrique Pérez Herrero_, Sep 25 2009]
%F A161886 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]
%e A161886 The 4x4 Redheffer matrix:
%e A161886   1,1,1,1
%e A161886   1,1,0,0
%e A161886   1,0,1,0
%e A161886   1,1,0,1
%e A161886 contains 11 nonzero elements.
%t A161886 A161886[n_] := Plus @@ Table[DivisorSigma[0, i], {i, 1, n}] + n - 1 (* _Enrique Pérez Herrero_, Sep 25 2009 *)
%t A161886 A161886[n_] := Total[Table[ Boole[Divisible[i, j] || (i == 1)], {i, 1, n}, {j, 1, n}], Infinity] (* _Enrique Pérez Herrero_, Sep 25 2009 *)
%t A161886 A161889[n_] := Plus @@ Plus @@ Table[Boole[Divisible[i, j] || (i == 1)], {i, 1, n}, {j, 1, n}] (* _Enrique Pérez Herrero_, Sep 28 2009 *)
%t A161886 A161889[n_] := Sum[Ceiling[n/i], {i, 1, n}] + DivisorSigma[0, n] - 1 (* _Enrique Pérez Herrero_, Sep 28 2009 *)
%o A161886 (Python)
%o A161886 from math import isqrt
%o A161886 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
%Y A161886 Cf. A143104, A006590, A000005.
%K A161886 nonn
%O A161886 1,2
%A A161886 _Mats Granvik_, Jun 21 2009
%E A161886 Edited by _N. J. A. Sloane_, Jun 26 2009