A326687 Sum of the second largest parts in 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, 3, 5, 6, 8, 14, 14, 19, 26, 34, 38, 49, 53, 70, 81, 96, 105, 139, 140, 187, 204, 246, 263, 326, 341, 437, 452, 543, 562, 715, 700, 898, 904, 1100, 1101, 1387, 1343, 1720, 1643, 2037, 1982

Offset

0,21

Links

Table of n, a(n) for n=0..61.

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) * i, where c is the prime characteristic (A010051).

a(n) = A326678(n) - A326679(n) - A326680(n) - A326681(n) - A326682(n) - A326683(n) - A326684(n) - A326685(n) - A326686(n) - A326688(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&][[All, 2]]], {n, 0, 70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 04 2021 *)

Crossrefs

Cf. A010051, A259201, A326678, A326679, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326688.

Sequence in context: A307637 A326462 A326548 * A352524 A172993 A335755

Adjacent sequences: A326684 A326685 A326686 * A326688 A326689 A326690

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 17 2019

Status

approved