A326543 Sum of the seventh largest parts of the partitions of n into 9 primes.

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, 15, 21, 22, 26, 26, 38, 36, 49, 47, 60, 59, 84, 73, 103, 95, 127, 111, 163, 132, 194, 163, 229, 196, 285, 220, 342, 278, 398, 316, 477, 366, 566, 427, 640, 494, 768, 557

Offset

0,19

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = A326540(n) - A326541(n) - A326542(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).

Mathematica

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

Crossrefs

Cf. A010051, A259200, A326540, A326541, A326542, A326544, A326545, A326546, A326547, A326548, A326549.

Sequence in context: A326681 A308975 A326457 * A326682 A097196 A132325

Adjacent sequences: A326540 A326541 A326542 * A326544 A326545 A326546

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved