A308924 - OEIS

%I #12 Oct 01 2021 15:43:12

%S 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,

%T 60,94,74,121,112,154,136,194,162,253,205,289,246,382,283,457,365,533,

%U 415,652,475,778,554,857,642,1048,690,1195,835,1345,944,1564

%N Sum of the second largest parts in the partitions of n into 6 primes.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

%F a(n) = A308919(n) - A308920(n) - A308921(n) - A308922(n) - A308923(n) - A308925(n).

%t 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 *)

%Y Cf. A010051, A259196, A308919, A308920, A308921, A308922, A308923, A308925.

%K nonn

%O 0,13

%A _Wesley Ivan Hurt_, Jun 30 2019