|
|
A309405
|
|
Number of prime parts in the partitions of n into 3 parts.
|
|
1
|
|
|
0, 0, 0, 0, 1, 3, 5, 7, 8, 12, 12, 16, 17, 21, 22, 29, 29, 34, 35, 41, 42, 50, 50, 58, 59, 67, 68, 77, 78, 86, 87, 96, 97, 108, 108, 119, 120, 130, 131, 144, 144, 155, 156, 168, 169, 182, 183, 197, 198, 212, 213, 228, 228, 242, 243, 258, 259, 275, 275, 291
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Figure 1: The partitions of n into 3 parts for n = 3, 4, ...
1+1+8
1+1+7 1+2+7
1+2+6 1+3+6
1+1+6 1+3+5 1+4+5
1+1+5 1+2+5 1+4+4 2+2+6
1+1+4 1+2+4 1+3+4 2+2+5 2+3+5
1+1+3 1+2+3 1+3+3 2+2+4 2+3+4 2+4+4
1+1+1 1+1+2 1+2+2 2+2+2 2+2+3 2+3+3 3+3+3 3+3+4 ...
-----------------------------------------------------------------------
n | 3 4 5 6 7 8 9 10 ...
-----------------------------------------------------------------------
a(n) | 0 1 3 5 7 8 12 12 ...
-----------------------------------------------------------------------
|
|
MATHEMATICA
|
Table[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|