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

0,21

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

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).

Mathematica

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

Crossrefs

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

Sequence in context: A353711 A008331 A173388 * A326541 A326680 A326456

Adjacent sequences: A326676 A326677 A326678 * A326680 A326681 A326682

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 17 2019

Status

approved