A308953 Sum of all the parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 7, 8, 18, 20, 44, 60, 104, 126, 180, 224, 340, 396, 551, 640, 882, 1034, 1357, 1536, 2025, 2314, 2943, 3304, 4176, 4680, 5797, 6464, 7887, 8806, 10605, 11664, 14023, 15504, 18291, 20040, 23657, 25956, 30272, 32956, 38295, 41860, 48269

Offset

0,8

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = 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, where mu is the Möbius function (A008683).

a(n) = n * A308952(n).

a(n) = A308954(n) + A308955(n) + A308956(n) + A308957(n) + A308958(n) + A308959(n) + A308960(n).

Mathematica

Table[Total[Flatten[Select[IntegerPartitions[n, {7}], AllTrue[#, SquareFreeQ]&]]], {n, 0, 50}] (* Harvey P. Dale, Feb 25 2024 *)

Crossrefs

Cf. A008683, A308952, A308954, A308955, A308956, A308957, A308958, A308959, A308960.

Sequence in context: A214788 A155946 A144614 * A143504 A322636 A309482

Adjacent sequences: A308950 A308951 A308952 * A308954 A308955 A308956

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 03 2019

Status

approved