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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,21
LINKS
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 *)
CROSSREFS
Sequence in context: A173388 A326679 A326541 * A326456 A326542 A326681
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 17 2019
STATUS
approved

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Last modified April 10 01:29 EDT 2024. Contains 371563 sequences. (Running on oeis4.)