OFFSET
1,3
COMMENTS
Total area of all y X z rectangles such that x + y = n, with x and y integers, 0 < x <= y and z = floor(y/x). - Wesley Ivan Hurt, Dec 21 2020
FORMULA
a(n) ~ n^2*(log(n) + 2*EulerGamma - Pi^2/12 - 3/2). - Rok Cestnik, Dec 20 2020
MATHEMATICA
Table[Sum[(n - k)*Floor[(n - k)/k], {k, Floor[n/2]}], {n, 60}]
PROG
(PARI) a(n) = sum(k=1, n\2, (n-k) * ((n-k)\k)); \\ Michel Marcus, Dec 02 2020
(Python)
from math import isqrt
def A339370(n): return n*(1-n)+(s:=isqrt(n))**2*(s+1-(n<<1))-sum((q:=n//k)*((k-(n<<1)<<1)+q+1) for k in range(1, s+1))>>1 # Chai Wah Wu, Oct 27 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 01 2020
STATUS
approved