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A309466 Sum of the prime parts in the partitions of n into 5 parts. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

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).

EXAMPLE

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

MATHEMATICA

Table[Sum[Sum[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + k (PrimePi[k] - PrimePi[k - 1]) + l (PrimePi[l] - PrimePi[l - 1]) + (n - i - j - k - l) (PrimePi[n - i - j - k - l] - PrimePi[n - i - j - k - l - 1]), {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]

CROSSREFS

Cf. A010051, A309427.

Sequence in context: A024481 A024591 A309465 * A309467 A309468 A309469

Adjacent sequences:  A309463 A309464 A309465 * A309467 A309468 A309469

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 03 2019

STATUS

approved

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Last modified October 21 22:35 EDT 2021. Contains 348156 sequences. (Running on oeis4.)