A308921 - OEIS

A308921

Sum of the fifth largest parts in the partitions of n into 6 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 7, 9, 7, 9, 12, 14, 14, 18, 18, 24, 27, 31, 30, 43, 33, 50, 48, 61, 53, 75, 62, 93, 71, 100, 87, 134, 92, 148, 113, 170, 127, 202, 139, 232, 159, 257, 190, 314, 190, 343, 233, 392, 264, 452, 275, 520, 308

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,13

LINKS

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

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(m) * c(l) * c(k) * c(j) * c(i) * c(n-i-k-j-l-m) * l, where c = A010051.

a(n) = A308919(n) - A308920(n) - A308922(n) - A308923(n) - A308924(n) - A308925(n).

MATHEMATICA

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

CROSSREFS

Cf. A010051, A259196, A308919, A308920, A308922, A308923, A308924, A308925.

Sequence in context: A365541 A308855 A301588 * A308977 A326459 A326545

Adjacent sequences: A308918 A308919 A308920 * A308922 A308923 A308924

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 30 2019

STATUS

approved