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A326678
Sum of all the 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, 20, 21, 22, 46, 48, 75, 104, 108, 140, 203, 240, 279, 352, 363, 476, 560, 648, 740, 950, 936, 1240, 1353, 1596, 1677, 2112, 2115, 2714, 2773, 3312, 3381, 4350, 4080, 5304, 5194, 6372, 6270, 8008
OFFSET
0,21
FORMULA
a(n) = 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), where c = A010051.
a(n) = n * A259201(n).
a(n) = A326679(n) + A326680(n) + A326681(n) + A326682(n) + A326683(n) + A326684(n) + A326685(n) + A326686(n) + A326687(n) + A326688(n).
MATHEMATICA
Table[Total[Flatten[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&]]], {n, 0, 60}] (* Harvey P. Dale, Jan 31 2024 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 17 2019
STATUS
approved