A309466 Sum of the prime parts in the partitions of n into 5 parts.

0, 0, 0, 0, 0, 0, 2, 7, 11, 28, 41, 67, 88, 136, 169, 248, 295, 413, 496, 652, 772, 1001, 1161, 1469, 1697, 2096, 2398, 2923, 3316, 3975, 4501, 5302, 5955, 6953, 7757, 8994, 9988, 11450, 12674, 14427, 15883, 17992, 19741, 22176, 24268, 27149, 29569, 32919

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Examples

			The partitions of n into 5 parts for n = 10, 11, ..
                                                       1+1+1+1+10
                                                        1+1+1+2+9
                                                        1+1+1+3+8
                                                        1+1+1+4+7
                                                        1+1+1+5+6
                                            1+1+1+1+9   1+1+2+2+8
                                            1+1+1+2+8   1+1+2+3+7
                                            1+1+1+3+7   1+1+2+4+6
                                            1+1+1+4+6   1+1+2+5+5
                                            1+1+1+5+5   1+1+3+3+6
                                1+1+1+1+8   1+1+2+2+7   1+1+3+4+5
                                1+1+1+2+7   1+1+2+3+6   1+1+4+4+4
                                1+1+1+3+6   1+1+2+4+5   1+2+2+2+7
                    1+1+1+1+7   1+1+1+4+5   1+1+3+3+5   1+2+2+3+6
                    1+1+1+2+6   1+1+2+2+6   1+1+3+4+4   1+2+2+4+5
                    1+1+1+3+5   1+1+2+3+5   1+2+2+2+6   1+2+3+3+5
        1+1+1+1+6   1+1+1+4+4   1+1+2+4+4   1+2+2+3+5   1+2+3+4+4
        1+1+1+2+5   1+1+2+2+5   1+1+3+3+4   1+2+2+4+4   1+3+3+3+4
        1+1+1+3+4   1+1+2+3+4   1+2+2+2+5   1+2+3+3+4   2+2+2+2+6
        1+1+2+2+4   1+1+3+3+3   1+2+2+3+4   1+3+3+3+3   2+2+2+3+5
        1+1+2+3+3   1+2+2+2+4   1+2+3+3+3   2+2+2+2+5   2+2+2+4+4
        1+2+2+2+3   1+2+2+3+3   2+2+2+2+4   2+2+2+3+4   2+2+3+3+4
        2+2+2+2+2   2+2+2+2+3   2+2+2+3+3   2+2+3+3+3   2+3+3+3+3
--------------------------------------------------------------------------
  n  |     10          11          12          13          14        ...
--------------------------------------------------------------------------
a(n) |     41          67          88         136         169        ...
--------------------------------------------------------------------------
- _Wesley Ivan Hurt_, Sep 12 2019
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A309427, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

Programs

Mathematica

Table[Total[Select[Flatten[IntegerPartitions[n,{5}]],PrimeQ]],{n,0,50}] (* Harvey P. Dale, Dec 31 2021 *)

Formula

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + (n-i-j-k-l) * c(n-i-j-k-l)), where c is the prime characteristic (A010051).