A077026 a(n) = Sum_{k=1..n} floor(n/k + 1)-floor(n/k + 1/2).

1, 2, 2, 4, 3, 5, 5, 6, 6, 8, 6, 10, 9, 9, 9, 13, 11, 12, 12, 14, 14, 16, 12, 18, 17, 17, 17, 19, 17, 21, 21, 22, 20, 22, 20, 26, 26, 24, 22, 28, 25, 29, 27, 29, 29, 29, 27, 33, 33, 32, 32, 36, 30, 34, 34, 38, 38, 38, 34, 40, 39, 39, 37, 43, 41, 45, 43, 41, 41, 45, 43, 50, 48

Offset

1,2

Links

Table of n, a(n) for n=1..73.

Formula

Conjecture: Let f(a,b)=1, if (a+b) mod |a-b| != (a mod |a-b|)+(b mod |a-b|), and 0 otherwise. a(n) = Sum_{k=1..n-1} 1-f(n,k). - Benedict W. J. Irwin, Sep 22 2016

Example

[4/1+1]-[4/1+1/2] + [4/2+1]-[4/2+1/2] + [4/3+1]-[4/3+1/2] + [4/4+1]-[4/4+1/2] = 1+1+1+1 = 4.

Mathematica

Table[Sum[Floor[n/k + 1] - Floor[n/k + 1/2], {k, n}], {n, 73}] (* Michael De Vlieger, Sep 26 2016 *)

Prog

(PARI) a(n) = sum(k=1, n, floor(n/k + 1)-floor(n/k + 1/2)); \\ Michel Marcus, Sep 24 2016

Crossrefs

Sequence in context: A225381 A007728 A262991 * A060026 A329437 A318632

Adjacent sequences: A077023 A077024 A077025 * A077027 A077028 A077029

Keyword

nonn

Author

Clark Kimberling, Oct 18 2002

Extensions

Duplicate term at a(44) removed by Benedict W. J. Irwin, Sep 22 2016

Status

approved