A326545 Sum of the fifth largest parts in the partitions of n into 9 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 7, 9, 10, 12, 18, 17, 23, 24, 30, 30, 45, 43, 59, 60, 75, 75, 106, 94, 130, 124, 165, 152, 210, 180, 257, 229, 307, 278, 386, 320, 463, 400, 547, 464, 654, 539, 784, 643, 896, 749, 1081

Offset

0,19

Links

Table of n, a(n) for n=0..63.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} c(q) * c(p) * c(o) * c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l-m-o-p-q) * l, where c(n) is the prime characteristic (A010051).

a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326544(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, PrimeQ]&][[All, 5]]], {n, 0, 70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 09 2021 *)

Crossrefs

Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326546, A326547, A326548, A326549.

Sequence in context: A308921 A308977 A326459 * A326684 A366598 A350457

Adjacent sequences: A326542 A326543 A326544 * A326546 A326547 A326548

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved