login
A326680
Sum of the ninth largest parts of 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, 2, 4, 4, 6, 8, 8, 10, 15, 17, 19, 23, 24, 30, 34, 38, 44, 54, 53, 67, 73, 83, 87, 105, 107, 131, 136, 156, 161, 200, 186, 233, 232, 275, 271, 335, 315, 398, 373, 456, 439, 550, 493, 636, 589
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) * q, where c = A010051.
a(n) = A326678(n) - A326679(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, 9]]], {n, 0, 70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 01 2019 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 17 2019
STATUS
approved