A308920 Sum of the smallest 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, 6, 9, 6, 9, 10, 14, 12, 18, 14, 24, 20, 29, 22, 41, 24, 48, 34, 57, 36, 69, 40, 85, 48, 90, 54, 120, 58, 132, 70, 150, 76, 176, 82, 202, 94, 221, 106, 266, 108, 293, 128, 328, 140, 366, 146, 426, 162, 450

Offset

0,13

Links

Table of n, a(n) for n=0..64.

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) * m, where c = A010051.

a(n) = A308919(n) - A308921(n) - A308922(n) - A308923(n) - A308924(n) - A308925(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[m*(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, A308921, A308922, A308923, A308924, A308925.

Sequence in context: A326682 A097196 A132325 * A308976 A326458 A326544

Adjacent sequences: A308917 A308918 A308919 * A308921 A308922 A308923

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 30 2019

Status

approved