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

Author

Ilya Gutkovskiy, Mar 11 2018

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000
• Index entries for sequences related to compositions

Crossrefs

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

Programs

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}]