OFFSET
0,43
COMMENTS
To illustrate the definition, the sum of primes indexed by all parts greater than one of the partition (5,2,2,1) is prime(5) + prime(2) + prime(2) = 17.
EXAMPLE
Triangle begins:
1
1
1 0 0 1
1 0 0 1 0 1
1 0 0 1 0 1 1 1
1 0 0 1 0 1 1 1 1 0 0 1
1 0 0 1 0 1 1 1 1 1 2 1 0 1
1 0 0 1 0 1 1 1 1 1 2 2 1 1 1 0 0 1
1 0 0 1 0 1 1 1 1 1 2 2 2 3 2 0 2 1 0 1
1 0 0 1 0 1 1 1 1 1 2 2 2 3 3 2 2 2 2 1 1 0 0 1
1 0 0 1 0 1 1 1 1 1 2 2 2 3 3 3 4 4 2 3 2 0 3 1 0 0 0 0 0 1
1 0 0 1 0 1 1 1 1 1 2 2 2 3 3 3 4 5 4 4 3 3 3 2 3 0 1 0 0 1 0 1
The T(8,13) = 3 partitions are: (6,1,1), (4,2,2), (3,3,2).
The T(10,17) = 4 partitions are: (7,1,1,1), (5,2,2,1), (4,4,2), (4,3,3).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Total[Select[Prime/@#, OddQ]]==k&]], {n, 0, 10}, {k, 0, If[n<=1, 0, Prime[n]]}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 01 2023
STATUS
approved