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A308924
Sum of the second largest parts in the partitions of n into 6 primes.
6
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 5, 6, 8, 14, 11, 16, 20, 28, 27, 38, 35, 52, 51, 66, 60, 94, 74, 121, 112, 154, 136, 194, 162, 253, 205, 289, 246, 382, 283, 457, 365, 533, 415, 652, 475, 778, 554, 857, 642, 1048, 690, 1195, 835, 1345, 944, 1564
OFFSET
0,13
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m) * i, where c = A010051.
a(n) = A308919(n) - A308920(n) - A308921(n) - A308922(n) - A308923(n) - A308925(n).
MATHEMATICA
Table[Total[Select[IntegerPartitions[n, {6}], AllTrue[#, PrimeQ]&][[All, 2]]], {n, 0, 60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 29 2021 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 30 2019
STATUS
approved