A286002 a(n) = 2n - d(n), where d(n) is the number of divisors of n (A000005).

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, 48, 50, 50, 56, 52, 60, 58, 62, 64, 66, 63, 72, 72, 74, 72, 80, 76, 84, 82, 84, 88, 92, 86, 95, 94, 98, 98, 104, 100, 106, 104, 110, 112, 116

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..59.

Formula

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

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

a(n) = A005843(n) - A000005(n). - Felix Fröhlich, Jun 11 2017

Maple

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

Mathematica

Table[2 n - DivisorSigma[0, n], {n, 100}]; (* Vincenzo Librandi, Jun 12 2017 *)

Prog

(PARI) a(n) = 2*n - numdiv(n)
(Magma) [2*n - NumberOfDivisors(n): n in [1..100]]; // Vincenzo Librandi, Jun 12 2017

Crossrefs

Cf. A000005, A005843, A049820.

Sequence in context: A369601 A345426 A061884 * A029935 A317625 A308447

Adjacent sequences: A285999 A286000 A286001 * A286003 A286004 A286005

Keyword

nonn

Author

Luc Rousseau, Jun 11 2017

Status

approved