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A309427 Number of prime parts in the partitions of n into 5 parts. 2
0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 24, 32, 46, 57, 77, 92, 118, 141, 175, 204, 249, 287, 342, 390, 459, 517, 600, 672, 771, 859, 975, 1078, 1214, 1336, 1495, 1636, 1818, 1982, 2190, 2378, 2615, 2830, 3097, 3340, 3641, 3915, 4250, 4557, 4930, 5273, 5687, 6068 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..52.

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)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(n-i-j-k-l)).

EXAMPLE

Figure 1: 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) |     17          24          32          46          57        ...

--------------------------------------------------------------------------

- Wesley Ivan Hurt, Sep 08 2019

MATHEMATICA

Table[Sum[Sum[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[k] - PrimePi[k - 1]) + (PrimePi[l] - PrimePi[l - 1]) + (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, A026811.

Sequence in context: A063693 A258713 A267517 * A211435 A049752 A286264

Adjacent sequences:  A309424 A309425 A309426 * A309428 A309429 A309430

KEYWORD

nonn,changed

AUTHOR

Wesley Ivan Hurt, Aug 01 2019

STATUS

approved

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Last modified September 21 11:45 EDT 2019. Contains 327253 sequences. (Running on oeis4.)