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A326679
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Sum of the smallest parts of 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, 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
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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) = 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.
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MATHEMATICA
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Table[Total[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&][[All, -1]]], {n, 0, 70}] (* Harvey P. Dale, Jan 20 2022 *)
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CROSSREFS
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Cf. A010051, A259201, A326678, 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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