Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Nov 19 2021 12:17:58
%S 0,0,0,0,0,0,0,0,0,0,2,3,3,8,8,15,17,17,19,35,30,50,54,61,62,102,79,
%T 129,119,150,151,233,169,260,207,300,234,398,263,467,350,527,425,667,
%U 391,768,518,839,606,1039,636,1233,774,1294,918,1612,947,1844,1102
%N Sum of the largest parts in the partitions of n into 5 primes.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l) * (n-i-j-k-l), where c = A010051.
%F a(n) = A308854(n) - A308855(n) - A308856(n) - A308857(n) - A308858(n).
%t Table[Sum[Sum[Sum[Sum[(n-i-j-k-l) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i - j - k - l] - PrimePi[n - i - j - k - l - 1]), {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]
%Y Cf. A010051, A259195, A308854, A308855, A308856, A308857, A308858.
%K nonn
%O 0,11
%A _Wesley Ivan Hurt_, Jun 28 2019