|
| |
|
|
A320638
|
|
Triangle T(n,k) read by rows: the number of partitions of n into k parts which are divisors of n.
|
|
1
|
|
|
|
1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 7, 8, 8, 6, 4, 3, 2, 1, 1, 1, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,18
|
|
|
LINKS
|
Table of n, a(n) for n=1..83.
|
|
|
FORMULA
|
T(n,n) = T(n,1) =1; representing partitions into the trivial divisors.
|
|
|
EXAMPLE
|
The triangle starts
1
1 1
1 0 1
1 1 1 1
1 0 0 0 1
1 1 2 2 1 1
1 0 0 0 0 0 1
1 1 1 2 2 1 1 1
1 0 1 0 1 0 1 0 1
1 1 0 1 2 2 1 1 1 1
1 0 0 0 0 0 0 0 0 0 1
1 1 3 7 8 8 6 4 3 2 1 1
1 0 0 0 0 0 0 0 0 0 0 0 1
1 1 0 0 1 1 2 2 1 1 1 1 1 1
1 0 1 0 3 0 3 0 2 0 2 0 1 0 1
1 1 1 2 3 4 4 4 4 3 2 2 2 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 2 3 6 8 9 10 9 8 6 5 4 3 2 2 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 1 3 6 8 10 10 9 9 8 6 5 4 3 3 2 1 1 1
1 0 1 0 1 0 3 0 3 0 2 0 2 0 2 0 1 0 1 0 1
1 1 0 0 0 0 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 3 9 20 33 44 50 51 48 42 36 29 23 18 14 11 8 6 4 3 2 1 1
|
|
|
MAPLE
|
A320638 := proc(n, noprts)
local a, p, w, el ;
a := 0 ;
for p in combinat[partition](n) do
if nops(p) = noprts then
w := true ;
for el in p do
if modp(n, el) <> 0 then
w := false;
break;
end if;
end do:
if w then
a := a+1 ;
end if;
end if ;
end do:
a ;
end proc:
seq(seq(A320638(n, k), k=1..n), n=1..13) ;
|
|
|
CROSSREFS
|
Cf. A018818 (row sums), A008284.
Sequence in context: A004562 A261817 A123550 * A262045 A263087 A204433
Adjacent sequences: A320635 A320636 A320637 * A320639 A320640 A320641
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. J. Mathar, Oct 18 2018
|
|
|
STATUS
|
approved
|
| |
|
|
