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A326679
Sum of the smallest 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, 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
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 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 17 2019
STATUS
approved