A326678 - OEIS

A326678

Sum of all the parts in the partitions of n into 10 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 21, 22, 46, 48, 75, 104, 108, 140, 203, 240, 279, 352, 363, 476, 560, 648, 740, 950, 936, 1240, 1353, 1596, 1677, 2112, 2115, 2714, 2773, 3312, 3381, 4350, 4080, 5304, 5194, 6372, 6270, 8008

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OFFSET

0,21

LINKS

Table of n, a(n) for n=0..56.

Index entries for sequences related to partitions

FORMULA

a(n) = 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)} c(r) * 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-r), where c = A010051.

a(n) = n * A259201(n).

a(n) = A326679(n) + A326680(n) + A326681(n) + A326682(n) + A326683(n) + A326684(n) + A326685(n) + A326686(n) + A326687(n) + A326688(n).

MATHEMATICA

Table[Total[Flatten[Select[IntegerPartitions[n, {10}], AllTrue[#, PrimeQ]&]]], {n, 0, 60}] (* Harvey P. Dale, Jan 31 2024 *)

CROSSREFS

Cf. A010051, A259201, A326679, A326680, A326681, A326682, A326683, A326684, A326685, A326686, A326687, A326688.

Sequence in context: A138602 A346400 A347298 * A347469 A030605 A125663

Adjacent sequences: A326675 A326676 A326677 * A326679 A326680 A326681

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 17 2019

STATUS

approved