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A326678
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Sum of all the parts in the partitions of n into 10 primes.
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10
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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
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OFFSET
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0,21
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LINKS
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FORMULA
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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.
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MATHEMATICA
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Table[Total[Flatten[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&]]], {n, 0, 60}] (* Harvey P. Dale, Jan 31 2024 *)
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CROSSREFS
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Cf. A010051, A259201, A326679, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326687, A326688.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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