A326682 Sum of the seventh largest parts of 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, 8, 9, 11, 16, 18, 21, 25, 26, 32, 38, 42, 49, 59, 60, 74, 84, 94, 103, 124, 127, 154, 163, 186, 194, 239, 229, 285, 285, 337, 342, 421, 398, 504, 477, 586, 566, 709, 640, 828, 768

Offset

0,21

Links

Table of n, a(n) for n=0..65.

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) * o, where c = A010051.

a(n) = A326678(n) - A326679(n) - A326680(n) - A326681(n) - A326683(n) - A326684(n) - A326685(n) - A326686(n) - A326687(n) - A326688(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o * (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[o] - PrimePi[o - 1]) (PrimePi[p] - PrimePi[p - 1]) (PrimePi[q] - PrimePi[q - 1]) (PrimePi[r] - PrimePi[r - 1]) (PrimePi[n - i - j - k - l - m - o - p - q - r] - PrimePi[n - i - j - k - l - m - o - p - q - r - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]

Crossrefs

Cf. A010051, A259201, A326678, A326679, A326680, A326681, A326683, A326684, A326685, A326686, A326687, A326688.

Sequence in context: A308975 A326457 A326543 * A097196 A132325 A308920

Adjacent sequences: A326679 A326680 A326681 * A326683 A326684 A326685

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 17 2019

Status

approved