A308854 Sum of all the parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 26, 28, 45, 48, 51, 54, 95, 80, 126, 132, 161, 144, 250, 182, 297, 252, 348, 330, 527, 352, 594, 442, 700, 504, 888, 570, 1053, 720, 1189, 882, 1505, 836, 1710, 1104, 1927, 1248, 2303, 1300, 2703, 1560, 2862, 1836

Offset

0,11

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to partitions

Formula

a(n) = n * Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l), where c = A010051.

a(n) = n * A259195(n).

a(n) = A308855(n) + A308856(n) + A308857(n) + A308858(n) + A308859(n).

Mathematica

Table[Total[Flatten[Select[IntegerPartitions[n, {5}], AllTrue[#, PrimeQ]&]]], {n, 0, 60}] (* Harvey P. Dale, Apr 18 2022 *)

Crossrefs

Cf. A010051, A259195, A308855, A308856, A308857, A308858, A308859.

Sequence in context: A235828 A102695 A252481 * A144582 A048024 A048002

Adjacent sequences: A308851 A308852 A308853 * A308855 A308856 A308857

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 28 2019

Status

approved