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A327766
Number of compositions (ordered partitions) of n into divisors of n that are at most sqrt(n).
1
1, 1, 1, 1, 5, 1, 13, 1, 34, 19, 89, 1, 927, 1, 610, 189, 4930, 1, 35890, 1, 46754, 1873, 28657, 1, 3919944, 571, 196418, 18560, 4205249, 1, 110187694, 1, 39882198, 183916, 9227465, 9496, 14484956252, 1, 63245986, 1822473, 11969319436, 1, 141930520462, 1, 34020543362, 339200673
OFFSET
0,5
FORMULA
a(n) = [x^n] 1 / (1 - Sum_{d|n, d <= sqrt(n)} x^d).
a(p) = 1, where p is prime.
MATHEMATICA
a[n_] := SeriesCoefficient[1/(1 - Sum[Boole[d <= Sqrt[n]] x^d, {d, Divisors[n]}]), {x, 0, n}]; Table[a[n], {n, 0, 45}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 24 2019
STATUS
approved