proposed

approved

editing

proposed

a(n) = A308953(n) - A308955(n) - A308956(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).

Cf. A008683, A308952, A308953, A308955, A308956, A308957, A308958, A308959, A308960.

allocated for Wesley Ivan HurtSum of the smallest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 10, 13, 15, 22, 25, 33, 37, 49, 55, 71, 77, 98, 109, 136, 148, 182, 199, 243, 264, 314, 344, 413, 441, 522, 567, 663, 711, 829, 896, 1036, 1106, 1269, 1370, 1572, 1666, 1903, 2041, 2316, 2460, 2780, 2971, 3350, 3546

0,10

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o)^2 * o, where mu is the Möbius function (A008683).

Table[Sum[Sum[Sum[Sum[Sum[Sum[o * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2 * MoebiusMu[n - i - j - k - l - m - o]^2, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Cf. A008683, A308952.

allocated

nonn

Wesley Ivan Hurt, Jul 03 2019

approved

editing

allocated for Wesley Ivan Hurt

recycled

allocated

recycled

approved