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A309405 Number of prime parts in the partitions of n into 3 parts. 1
0, 0, 0, 0, 1, 3, 5, 7, 8, 12, 12, 16, 17, 21, 22, 29, 29, 34, 35, 41, 42, 50, 50, 58, 59, 67, 68, 77, 78, 86, 87, 96, 97, 108, 108, 119, 120, 130, 131, 144, 144, 155, 156, 168, 169, 182, 183, 197, 198, 212, 213, 228, 228, 242, 243, 258, 259, 275, 275, 291 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..59.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (A010051(i) + A010051(j) + A010051(n-i-j)).

EXAMPLE

Figure 1: The partitions of n into 3 parts for n = 3, 4, ...

                                                          1+1+8

                                                   1+1+7  1+2+7

                                                   1+2+6  1+3+6

                                            1+1+6  1+3+5  1+4+5

                                     1+1+5  1+2+5  1+4+4  2+2+6

                              1+1+4  1+2+4  1+3+4  2+2+5  2+3+5

                       1+1+3  1+2+3  1+3+3  2+2+4  2+3+4  2+4+4

         1+1+1  1+1+2  1+2+2  2+2+2  2+2+3  2+3+3  3+3+3  3+3+4    ...

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

  n  |     3      4      5      6      7      8      9     10      ...

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

a(n) |     0      1      3      5      7      8     12     12      ...

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

MATHEMATICA

Table[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}]

CROSSREFS

Cf. A010051, A069905.

Sequence in context: A296233 A276112 A228075 * A032420 A127458 A039003

Adjacent sequences:  A309402 A309403 A309404 * A309406 A309407 A309408

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 30 2019

STATUS

approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)