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A300715 Number of compositions (ordered partitions) of n into squares that do not divide n. 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 3, 0, 0, 7, 6, 0, 0, 14, 10, 4, 0, 22, 20, 10, 0, 32, 39, 20, 0, 49, 70, 42, 0, 12, 116, 88, 0, 128, 156, 174, 11, 207, 3, 320, 0, 333, 551, 575, 0, 555, 914, 0, 0, 959, 1502, 1829, 44, 1691, 2486, 3192, 0, 3000, 4172, 4005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

EXAMPLE

a(21) = 4 because we have [9, 4, 4, 4], [4, 9, 4, 4], [4, 4, 9, 4] and [4, 4, 4, 9].

MAPLE

a:= proc(m) option remember; local b; b:= proc(n) option

      remember; `if`(n=0, 1, add((s->`if`(s>n or irem(m, s)

       =0, 0, b(n-s)))(j^2), j=2..isqrt(n))) end; b(m)

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 11 2018

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, 75}]

CROSSREFS

Cf. A000290, A006456, A294105, A294265, A294266, A300702, A300703, A300704, A300706.

Sequence in context: A226728 A244140 A091227 * A035444 A244141 A152489

Adjacent sequences:  A300712 A300713 A300714 * A300716 A300717 A300718

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 11 2018

STATUS

approved

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Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)