cp's OEIS Frontend

A309471 Sum of the prime parts in the partitions of n into 10 parts.

%I A309471 #11 Jan 07 2022 09:02:40
%S A309471 0,0,0,0,0,0,0,0,0,0,0,2,7,11,28,41,79,115,191,273,428,574,851,1133,
%T A309471 1576,2072,2819,3621,4812,6112,7918,9931,12655,15684,19714,24221,
%U A309471 29987,36534,44796,54051,65660,78684,94653,112671,134499,159012,188569,221650
%N A309471 Sum of the prime parts in the partitions of n into 10 parts.
%H A309471 David A. Corneth, <a href="/A309471/b309471.txt">Table of n, a(n) for n = 0..9999</a>
%H A309471 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309471 a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (r * c(r) + q * c(q) + p * c(p) + o * c(o) + m * c(m) + l * c(l) + k * c(k) + j * c(j) + i * c(i) + (n-i-j-k-l-m-o-p-q-r) * c(n-i-j-k-l-m-o-p-q-r)), where c is the prime characteristic (A010051).
%t A309471 Table[Sum[Sum[Sum[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]) + p (PrimePi[p] - PrimePi[p - 1]) + q (PrimePi[q] - PrimePi[q - 1]) + r (PrimePi[r] - PrimePi[r - 1]) + (n - i - j - k - l - m - o - p - q - r) (PrimePi[n - i - j - k - l - m - o - p - q - r] - PrimePi[n - i - j - k - l - m - o - p - q - r - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 80}]
%Y A309471 Cf. A010051, A309439, A309465, A309466, A309467, A309468, A309469, A309470, A309471.
%K A309471 nonn
%O A309471 0,12
%A A309471 _Wesley Ivan Hurt_, Aug 03 2019