A300706 Number of compositions (ordered partitions) of n into squarefree parts that do not divide n.

1, 0, 0, 0, 0, 2, 0, 5, 2, 5, 2, 27, 2, 67, 12, 16, 28, 366, 4, 848, 28, 182, 153, 4591, 20, 4172, 554, 2217, 558, 57695, 6, 134118, 3834, 14629, 6972, 97478, 258, 1684852, 24467, 120869, 5308, 9104710, 189, 21165023, 124427, 117017, 297830, 114373157, 3394, 126979537, 72158, 7655405

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Index entries for sequences related to compositions

Example

a(18) = 4 because we have [13, 5], [11, 7], [7, 11] and [5, 13].

Maple

with(numtheory):
a:= proc(m) option remember; local b; b:= proc(n) option
      remember; `if`(n=0, 1, add(`if`(not issqrfree(j) or
       irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Mar 11 2018

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && SquareFreeQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 51}]

Crossrefs

Cf. A005117, A280194, A284464, A300585, A300586, A300702, A300703, A300704.

Sequence in context: A267213 A261805 A300703 * A351481 A014842 A360559

Adjacent sequences: A300703 A300704 A300705 * A300707 A300708 A300709

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 11 2018

Status

approved