|
|
A366984
|
|
a(n) = Sum_{k=1..n} binomial(k+2,2) * floor(n/k).
|
|
3
|
|
|
3, 12, 25, 49, 73, 120, 159, 228, 296, 392, 473, 626, 734, 899, 1069, 1291, 1465, 1757, 1970, 2312, 2614, 2977, 3280, 3803, 4178, 4670, 5144, 5759, 6227, 6993, 7524, 8307, 8993, 9803, 10529, 11630, 12374, 13373, 14311, 15559, 16465, 17867, 18860, 20273, 21579, 23016
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^3 - 1) = 1/(1-x) * Sum_{k>0} binomial(k+2,2) * x^k/(1-x^k).
|
|
PROG
|
(PARI) a(n) = sum(k=1, n, binomial(k+2, 2)*(n\k));
(Python)
from math import isqrt
def A366984(n): return (-(s:=isqrt(n))*(s*(s*(s+7)+17)+17)+sum(((q:=n//w)+1)*(q*(q+5)+3*(w*(w+3)+4)) for w in range(1, s+1)))//6 # Chai Wah Wu, Oct 31 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|