A326540 Sum of all the parts in 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, 18, 19, 20, 42, 44, 69, 96, 100, 130, 189, 196, 261, 300, 341, 384, 528, 544, 700, 756, 888, 988, 1287, 1240, 1599, 1638, 2021, 2024, 2655, 2438, 3243, 3120, 3920, 3850, 4998, 4420, 6042, 5616, 7205, 6608

Offset

0,19

Links

Table of n, a(n) for n=0..56.

Index entries for sequences related to partitions

Formula

a(n) = 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)} 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), where c = A010051.

a(n) = n * A259200(n).

a(n) = A326541(n) + A326542(n) + A326543(n) + A326544(n) + A326545(n) + A326546(n) + A326547(n) + A326548(n) + A326549(n).

Mathematica

Table[n * Sum[Sum[Sum[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[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, A326541, A326542, A326543, A326544, A326545, A326546, A326547, A326548, A326549.

Sequence in context: A270044 A018823 A025144 * A241267 A241848 A146331

Adjacent sequences: A326537 A326538 A326539 * A326541 A326542 A326543

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved