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A368872
Number of compositions (ordered partitions) of n into prime parts not greater than sqrt(n).
0
1, 0, 0, 0, 1, 0, 1, 0, 1, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 2652, 3769, 5413, 7713, 11031, 15778, 22513, 32222, 46004, 65766, 94004, 134283, 191992, 274291, 392041, 560287, 800615, 1144320, 1635193, 2336976, 3339800, 4772784, 6821096
OFFSET
0,10
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, add(
`if`(isprime(j), b(n-j, t), 0), j=1..min(n, t)))
end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..47); # Alois P. Heinz, Jan 13 2024
MATHEMATICA
Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeQ[k]] x^k, {k, 1, Floor[Sqrt[n]]}]), {x, 0, n}], {n, 0, 47}]
CROSSREFS
Sequence in context: A159018 A361415 A345980 * A369221 A005427 A116024
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 08 2024
STATUS
approved