OFFSET
1,2
COMMENTS
a(n) is the sum of all divisors d of k such that d^2 <= k where k ranges from 1 to n.
FORMULA
a(n) = m*(6*n+5-m*(2*m+3))/6 + Sum_{k=1..n, i=1..floor(sqrt(k))} [(k-1) mod i] - [k mod i] where m = floor(sqrt(n)).
a(n) = m*(6*n+5-m*(2*m+3))/6 + Sum_{k=1..n, i=1..floor(sqrt(k))} (k-1) mod i - Sum_{k=1..n} A176314(k) where m = floor(sqrt(n)).
MATHEMATICA
Table[Select[Divisors[n], # <= Sqrt[n]&]//Total, {n, 1, 60}]//Accumulate (* Jean-François Alcover, Jan 26 2024 *)
PROG
(Python)
from itertools import takewhile
from sympy import divisors
def A359503(n): return sum(sum(takewhile(lambda x:x**2<=i, divisors(i))) for i in range(1, n+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jan 24 2024
STATUS
approved