A309468 - OEIS

%I #12 Jan 07 2022 14:01:37

%S 0,0,0,0,0,0,0,0,2,7,11,28,41,79,115,175,238,357,464,670,851,1145,

%T 1441,1908,2349,3034,3698,4657,5635,7007,8350,10240,12124,14609,17192,

%U 20549,23920,28326,32802,38437,44287,51520,58934,68170,77621,89049,100981

%N Sum of the prime parts in the partitions of n into 7 parts.

%H David A. Corneth, <a href="/A309468/b309468.txt">Table of n, a(n) for n = 0..9999</a>

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

%F a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} (i * c(i) + j * c(j) + k * c(k) + l * c(l) + m * c(m) + o * c(o) + (n-i-j-k-l-m-o) * c(n-i-j-k-l-m-o)), where c = A010051.

%t Table[Sum[Sum[Sum[Sum[Sum[Sum[i (PrimePi[i] - PrimePi[i - 1]) + j (PrimePi[j] - PrimePi[j - 1]) + k (PrimePi[k] - PrimePi[k - 1]) + l (PrimePi[l] - PrimePi[l - 1]) + m (PrimePi[m] - PrimePi[m - 1]) + o (PrimePi[o] - PrimePi[o - 1]) + (n - i - j - k - l - m - o) (PrimePi[n - i - j - k - l - m - o] - PrimePi[n - i - j - k - l - m - o - 1]), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 80}]

%Y Cf. A010051, A309436, A309465, A309466, A309467, A309468, A309469, A309470, A309471.

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Aug 03 2019