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A326549 Sum of the largest parts of the partitions of n into 9 primes. 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 8, 8, 15, 20, 20, 27, 43, 47, 67, 78, 85, 104, 144, 152, 202, 223, 254, 298, 385, 387, 485, 509, 609, 640, 827, 775, 1017, 1015, 1230, 1265, 1584, 1445, 1944, 1852, 2301, 2200, 2840, 2565, 3439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,19

LINKS

Table of n, a(n) for n=0..59.

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)} A010051(q) * A010051(p) * A010051(o) * A010051(m) * A010051(l) * A010051(k) * A010051(j) * A010051(i) * A010051(n-i-j-k-l-m-o-p-q) * (n-i-j-k-l-m-o-p-q).

a(n) = A326540(n) - A326541(n) -  A326542(n) - A326543(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o-p-q) * (PrimePi[i] - PrimePi[i - 1]) (PrimePi[j] - PrimePi[j - 1]) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[l] - PrimePi[l - 1]) (PrimePi[m] - PrimePi[m - 1]) (PrimePi[o] - PrimePi[o - 1]) (PrimePi[p] - PrimePi[p - 1]) (PrimePi[q] - PrimePi[q - 1]) (PrimePi[n - i - j - k - l - m - o - p - q] - PrimePi[n - i - j - k - l - m - o - p - q - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

CROSSREFS

Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326545, A326546, A326547, A326548.

Sequence in context: A308925 A308980 A326463 * A326688 A011155 A161136

Adjacent sequences:  A326546 A326547 A326548 * A326550 A326551 A326552

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 13 2019

STATUS

approved

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)