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A326542
Sum of the eighth largest parts of the partitions of n into 9 primes.
9
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, 11, 15, 15, 19, 22, 24, 26, 34, 36, 44, 47, 53, 59, 73, 71, 87, 93, 109, 109, 138, 128, 163, 157, 190, 190, 238, 210, 277, 262, 325, 300, 387, 344, 457, 399, 515, 464, 617, 515
OFFSET
0,19
FORMULA
a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} 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) * p, where c = A010051.
a(n) = A326540(n) - A326541(n) - A326543(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).
MATHEMATICA
Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, PrimeQ]&][[All, 8]]], {n, 0, 70}] (* Harvey P. Dale, May 03 2022 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 13 2019
STATUS
approved