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%I A355196 #6 Jun 25 2022 01:21:01
%S A355196 0,0,0,0,0,0,2,3,3,8,5,12,12,12,7,23,18,38,24,31,24,59,30,73,47,71,49,
%T A355196 113,55,115,40,102,59,171,48,168,100,191,102,220,50,265,89,246,120,
%U A355196 322,109,383,136,348,181,477,158,516,117,468,199,605,133,574,170,600,252,751,133
%N A355196 Sum of the largest parts of the partitions of n into exactly 3 prime parts.
%H A355196 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A355196 a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} c(i) * c(j) * c(n-i-j) * (n-i-j), where c = A010051.
%F A355196 a(n) = A355199(n) - A355197(n) - A355198(n).
%e A355196 a(9) = 8; since 9 can be written as the sum of 3 primes in two ways: 2+2+5 = 3+3+3 and the sum of the largest parts of these partitions is 5+3 = 8, we have a(9) = 8.
%t A355196 Table[Sum[Sum[(n - i - j) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[n - i - j] - PrimePi[n - i - j - 1]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}]
%Y A355196 Cf. A010051, A068307, A355197, A355198, A355199.
%K A355196 nonn
%O A355196 0,7
%A A355196 _Wesley Ivan Hurt_, Jun 23 2022

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