A326455 Sum of all the parts in the partitions of n into 8 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 17, 18, 38, 40, 63, 88, 92, 120, 150, 182, 216, 280, 261, 360, 434, 512, 528, 714, 665, 936, 962, 1178, 1170, 1560, 1394, 1932, 1849, 2332, 2160, 2990, 2632, 3696, 3234, 4250, 3927, 5408, 4452, 6372, 5445

Offset: 0

Author

Wesley Ivan Hurt, Jul 06 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259198, A326456, A326457, A326458, A326459, A326460, A326461, A326462, A326463.

Programs

Mathematica

a[n_] := n*Length[IntegerPartitions[n, {8}, Prime[Range[PrimePi[n]]]]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 07 2019 *)

Formula

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

a(n) = n * A259198(n).

a(n) = A326456(n) + A326457(n) + A326458(n) + A326459(n) + A326460(n) + A326461(n) + A326462(n) + A326463(n).