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A294105 Number of compositions (ordered partitions) of n into squares dividing n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A265656 A137296 A329291 * A101124 A011127 A172970
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 28 2017
STATUS
approved

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Last modified April 17 12:12 EDT 2024. Contains 371763 sequences. (Running on oeis4.)