A075995 a(n) = Sum_{k=1..floor(n/2)} floor(n/k) for n >= 2, with a(1) = 1.

1, 2, 3, 6, 7, 11, 12, 16, 18, 22, 23, 29, 30, 34, 37, 42, 43, 49, 50, 56, 59, 63, 64, 72, 74, 78, 81, 87, 88, 96, 97, 103, 106, 110, 113, 122, 123, 127, 130, 138, 139, 147, 148, 154, 159, 163, 164, 174, 176, 182, 185, 191, 192, 200, 203, 211, 214, 218, 219, 231, 232

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

a(6) = floor(6/1) + floor(6/2) + floor(6/3) = 11.

Mathematica

Table[If[n == 1, 1, Sum[Floor[n/i], {i, Floor[n/2]}]], {n, 80}] (* Wesley Ivan Hurt, Nov 26 2020 *)

Prog

(Python)
from math import isqrt
def A075995(n): return -(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1)-(n+1>>1) if n>1 else 1 # Chai Wah Wu, Oct 23 2023

Crossrefs

a(n) = A006218(n) - floor((n+1)/2) for n >= 2.

Sequence in context: A253239 A226384 A298947 * A102432 A024561 A350573

Adjacent sequences: A075992 A075993 A075994 * A075996 A075997 A075998

Keyword

nonn,easy

Author

Clark Kimberling, Sep 28 2002

Extensions

Name corrected by Wesley Ivan Hurt, Nov 26 2020

Status

approved