A309433 Number of prime parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 38, 57, 74, 103, 129, 173, 209, 267, 323, 402, 477, 583, 683, 820, 954, 1125, 1295, 1515, 1727, 1995, 2264, 2590, 2917, 3316, 3713, 4188, 4668, 5229, 5800, 6470, 7140, 7918, 8712, 9618, 10539, 11590, 12655, 13862

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259196, A309427.

Programs

Mathematica

Table[Count[Flatten[IntegerPartitions[n,{6}]],?PrimeQ],{n,0,50}] (* _Harvey P. Dale, Sep 03 2024 *)

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(m) + A010051(n-i-j-k-l-m)).