OFFSET
0,11
FORMULA
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (A010051(i) + A010051(j) + A010051(k) + A010051(l) + A010051(m) + A010051(o) + A010051(p) + A010051(n-i-j-k-l-m-o-p)).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[k] - PrimePi[k - 1]) + (PrimePi[l] - PrimePi[l - 1]) + (PrimePi[m] - PrimePi[m - 1]) + (PrimePi[o] - PrimePi[o - 1]) + (PrimePi[p] - PrimePi[p - 1]) + (PrimePi[n - i - j - k - l - m - o - p] - PrimePi[n - i - j - k - l - m - o - p - 1]), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
Table[Count[Flatten[IntegerPartitions[n, {8}]], _?PrimeQ], {n, 0, 50}] (* Harvey P. Dale, May 21 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 03 2019
STATUS
approved