A326460 - OEIS

A326460

Sum of the fourth largest parts of the partitions of n into 8 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 5, 7, 10, 10, 14, 15, 19, 20, 30, 26, 38, 43, 54, 51, 74, 64, 97, 93, 118, 111, 159, 132, 193, 172, 231, 202, 293, 243, 357, 296, 407, 352, 517, 402, 600, 495, 706, 577, 851, 661, 1004, 800, 1150

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OFFSET

0,17

LINKS

Table of n, a(n) for n=0..62.

Index entries for sequences related to partitions

FORMULA

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

a(n) = A326455(n) - A326456(n) - A326457(n) - A326458(n) - A326459(n) - A326461(n) - A326462(n) - A326463(n).

MATHEMATICA

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

CROSSREFS

Cf. A010051, A259198, A326455, A326456, A326457, A326458, A326459, A326461, A326462, A326463.

Sequence in context: A308856 A308922 A308978 * A326546 A326685 A274150

Adjacent sequences: A326457 A326458 A326459 * A326461 A326462 A326463

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 06 2019

STATUS

approved