|
|
A156745
|
|
a(n) = Sum_{k=1..n} floor((n+k)/k) = n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also a(n) = n + A006218(n).
|
|
3
|
|
|
2, 5, 8, 12, 15, 20, 23, 28, 32, 37, 40, 47, 50, 55, 60, 66, 69, 76, 79, 86, 91, 96, 99, 108, 112, 117, 122, 129, 132, 141, 144, 151, 156, 161, 166, 176, 179, 184, 189, 198, 201, 210, 213, 220, 227, 232, 235, 246, 250, 257, 262, 269, 272, 281, 286, 295, 300
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Generalized sequence b(n) = Sum_{k=1..n} floor((n+k*t)/k) = t*n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also b(n) = t*n + A006218(n).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*n + Sum_{k=1..floor(n/2)} floor((n-k)/k). - Wesley Ivan Hurt, Dec 25 2020
|
|
PROG
|
(PARI) a(n) = n + sum(k=1, n, numdiv(k)); \\ Michel Marcus, Oct 02 2020
(Python)
from math import isqrt
def A156745(n): return n-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1) # Chai Wah Wu, Oct 23 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|