A308974 Sum of all the parts in the partitions of n into 7 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 15, 16, 34, 36, 57, 80, 84, 88, 138, 144, 200, 208, 243, 280, 406, 360, 496, 512, 627, 646, 910, 792, 1110, 988, 1326, 1240, 1763, 1386, 2064, 1848, 2520, 2162, 3102, 2448, 3773, 3000, 4284, 3536, 5247, 3942

Offset: 0

Author

Wesley Ivan Hurt, Jul 04 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259197, A307637, A308975, A308976, A308977, A308978, A308979, A308980.

Programs

Mathematica

Table[Total[Flatten[Select[IntegerPartitions[n,{7}],AllTrue[#,PrimeQ]&]]],{n,0,60}] (* Harvey P. Dale, Nov 28 2023 *)

Formula

a(n) = 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)} c(i) * c(j) * c(k) * c(l) * c(m) * c(o) * c(n-i-j-k-l-m-o), c = A010051.

a(n) = n * A259197(n).

a(n) = A308975(n) + A308976(n) + A308977(n) + A308978(n) + A308979(n) + A307637(n) + A308980(n).