A326679 Sum of the smallest parts of the partitions of n into 10 primes.

0, 0, 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, 8, 10, 14, 17, 18, 23, 22, 30, 32, 38, 40, 54, 48, 67, 66, 83, 78, 105, 94, 131, 118, 154, 138, 198, 160, 231, 196, 271, 228, 329, 262, 392, 308, 446, 358, 536, 400, 620, 472

Offset: 0

Author

Wesley Ivan Hurt, Jul 17 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259201, A326678, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326687, A326688.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{10}],AllTrue[#,PrimeQ]&][[All,-1]]],{n,0,70}] (* Harvey P. Dale, Jan 20 2022 *)

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} c(r) * 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-r) * r, where c = A010051.

a(n) = A326678(n) - A326680(n) - A326681(n) - A326682(n) - A326683(n) - A326684(n) - A326685(n) - A326686(n) - A326687(n) - A326688(n).