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A368873
Number of compositions (ordered partitions) of n into nonprime parts not greater than sqrt(n).
0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 95, 131, 181, 250, 345, 476, 657, 907, 1252, 1728, 2385, 3292, 4544, 6272, 8657, 11949, 16493, 22765, 31422, 43371, 439373, 643932, 943728, 1383100, 2027032, 2970760, 4353861, 6380893, 9351653, 13705513, 20086406, 29438059
OFFSET
0,17
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, add(
`if`(isprime(j), 0, b(n-j, t)), 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: A057874 A112135 A369342 * A074237 A192180 A134217
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 08 2024
STATUS
approved