A294105 Number of compositions (ordered partitions) of n into squares dividing n.

1, 1, 1, 1, 2, 1, 1, 1, 7, 2, 1, 1, 26, 1, 1, 1, 96, 1, 12, 1, 345, 1, 1, 1, 1252, 2, 1, 76, 4544, 1, 1, 1, 17473, 1, 1, 1, 127654, 1, 1, 1, 217286, 1, 1, 1, 788674, 2490, 1, 1, 3182706, 2, 28, 1, 10390321, 1, 14128, 1, 37713313, 1, 1, 1, 136886433, 1, 1, 80396, 579739960, 1, 1, 1, 1803399103, 1, 1

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2500

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Example

a(8) = 7 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are squares {1, 4} therefore we have [4, 4], [4, 1, 1, 1, 1], [1, 4, 1, 1, 1], [1, 1, 4, 1, 1], [1, 1, 1, 4, 1], [1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1].

Maple

a:= proc(n) option remember; local b, l;
      l, b:= select(issqr, numtheory[divisors](n)),
      proc(m) option remember; `if`(m=0, 1,
         add(`if`(j>m, 0, b(m-j)), j=l))
      end; b(n)
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Oct 30 2017

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0 && IntegerQ[k^(1/2)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 70}]

Crossrefs

Cf. A006456, A046951, A100346, A284345.

Sequence in context: A265656 A137296 A329291 * A101124 A011127 A172970

Adjacent sequences: A294102 A294103 A294104 * A294106 A294107 A294108

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2017

Status

approved