|
|
A346018
|
|
Triangle read by rows: T(n,k) is the number of integers m such that 1 <= m <= n and gcd(m,n) <= k, 1 <= k <= n.
|
|
1
|
|
|
1, 1, 2, 2, 2, 3, 2, 3, 3, 4, 4, 4, 4, 4, 5, 2, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 4, 6, 6, 7, 7, 7, 7, 8, 6, 6, 8, 8, 8, 8, 8, 8, 9, 4, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 4, 6, 8, 10, 10, 11, 11, 11, 11, 11, 11, 12
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = n-1 for A032742(n) <= k <= n-1.
T(n,n) = n.
|
|
EXAMPLE
|
Triangle begins:
n\k 1 2 3 4 5 6 7 8 9 10
----------------------------------
1: 1
2: 1 2
3: 2 2 3
4: 2 3 3 4
5: 4 4 4 4 5
6: 2 4 5 5 5 6
7: 6 6 6 6 6 6 7
8: 4 6 6 7 7 7 7 8
9: 6 6 8 8 8 8 8 8 9
10: 4 8 8 8 9 9 9 9 9 10
|
|
PROG
|
(PARI) T(n, k) = sum(m=1, n, gcd(m, n) <= k); \\ Michel Marcus, Jul 01 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|