A326683 Sum of the sixth largest parts in the partitions of n into 10 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 6, 9, 9, 12, 16, 20, 21, 27, 26, 36, 38, 47, 49, 68, 62, 86, 88, 111, 107, 145, 133, 183, 173, 220, 206, 287, 247, 341, 311, 411, 372, 509, 438, 610, 527, 713, 624, 865, 716, 1009

Offset

0,21

Links

Table of n, a(n) for n=0..64.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} c(r) * c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q-r) * m, where c = A010051.

a(n) = A326678(n) - A326679(n) - A326680(n) - A326681(n) - A326682(n) - A326684(n) - A326685(n) - A326686(n) - A326687(n) - A326688(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&][[All, 6]]], {n, 0, 70}] (* Harvey P. Dale, Aug 12 2021 *)

Crossrefs

Cf. A010051, A259201, A326678, A326679, A326680, A326681, A326682, A326684, A326685, A326686, A326687, A326688.

Sequence in context: A308976 A326458 A326544 * A239961 A365541 A308855

Adjacent sequences: A326680 A326681 A326682 * A326684 A326685 A326686

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 17 2019

Status

approved