|
|
A363327
|
|
Total number of parts coprime to n in the partitions of n into 9 parts.
|
|
7
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 9, 8, 18, 21, 45, 48, 88, 96, 198, 153, 369, 298, 542, 533, 1107, 673, 1695, 1375, 2280, 2017, 4392, 1962, 6588, 4668, 7337, 6695, 11924, 6703, 19746, 13220, 20416, 15497, 37854, 15056, 51372, 31987, 43358, 43930, 91404, 39701, 111571, 62525
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,9
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (c(i) + c(j) + c(k) + c(l) + c(m) + c(o) + c(p) + c(q) + c(n-i-j-k-l-m-o-p-q)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.
|
|
EXAMPLE
|
The partitions of 12 into 9 parts are: 1+1+1+1+1+1+1+1+4, 1+1+1+1+1+1+1+2+3, and 1+1+1+1+1+1+2+2+2. 12 is coprime to 1, but not 2, 3, or 4. Since there are 21 total parts in these partitions that are coprime to 12, a(12) = 21.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|