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A326687
Sum of the second largest parts in the partitions of n into 10 primes.
10
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
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 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 17 2019
STATUS
approved