A309433 - OEIS

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

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OFFSET

0,9

LINKS

Table of n, a(n) for n=0..50.

Index entries for sequences related to partitions

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)).

MATHEMATICA

Table[Sum[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[m] - PrimePi[m - 1]) + (PrimePi[n - i - j - k - l - m] - PrimePi[n - i - j - k - l - m - 1]), {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

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

CROSSREFS

Cf. A010051, A259196, A309427.

Sequence in context: A087732 A278053 A174916 * A309436 A309437 A309438

Adjacent sequences: A309430 A309431 A309432 * A309434 A309435 A309436

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 03 2019

STATUS

approved