A326456 Sum of the smallest 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, 4, 6, 8, 8, 11, 12, 15, 16, 22, 18, 26, 28, 36, 32, 47, 38, 59, 52, 71, 60, 93, 68, 109, 86, 128, 96, 157, 112, 190, 132, 210, 154, 262, 168, 300, 198, 344, 224, 399, 246, 464, 286, 515, 324, 605

Offset: 0

Author

Wesley Ivan Hurt, Jul 06 2019

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..199
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259198, A326455, A326457, A326458, A326459, A326460, A326461, A326462, A326463.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{8}],AllTrue[#,PrimeQ]&][[;;,-1]]],{n,0,70}] (* Harvey P. Dale, Mar 28 2025 *)

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) * p, where c = A010051.

a(n) = A326455(n) - A326457(n) - A326458(n) - A326459(n) - A326460(n) - A326461(n) - A326462(n) - A326463(n).