%I #69 Sep 08 2022 08:46:19

%S 1,2,4,5,8,8,12,12,15,16,20,18,24,24,26,27,32,30,36,34,38,40,44,40,47,

%T 48,50,50,56,52,60,58,62,64,66,63,72,72,74,72,80,76,84,82,84,88,92,86,

%U 95,94,98,98,104,100,106,104,110,112,116

%N a(n) = 2n - d(n), where d(n) is the number of divisors of n (A000005).

%C Let H_n denote the y=n/x (1<=x<=n) piece of the hyperbola. a(n) is the number of intersections between H_n and the Cartesian grid (Z X R union R X Z) and a(n)-1 is the number of (a,a+1) X (b,b+1) open unit squares, with a and b integers, crossed by H_n.

%F a(n) = 2n - A000005(n).

%F a(n) = n + A049820(n).

%F a(n) = A005843(n) - A000005(n). - _Felix Fröhlich_, Jun 11 2017

%p A286002:=n->2*n-numtheory[tau](n): seq(A286002(n), n=1..100); # _Wesley Ivan Hurt_, Jun 19 2017

%t Table[2 n - DivisorSigma[0, n], {n, 100}]; (* _Vincenzo Librandi_, Jun 12 2017 *)

%o (PARI) a(n) = 2*n - numdiv(n)

%o (Magma) [2*n - NumberOfDivisors(n): n in [1..100]]; // _Vincenzo Librandi_, Jun 12 2017

%Y Cf. A000005, A005843, A049820.

%K nonn

%O 1,2

%A _Luc Rousseau_, Jun 11 2017