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A300703
Number of compositions (ordered partitions) of n into prime parts that do not divide n.
4
1, 0, 0, 0, 0, 2, 0, 5, 2, 5, 2, 19, 2, 45, 6, 10, 14, 231, 4, 500, 14, 48, 45, 2351, 12, 1520, 144, 637, 100, 24441, 6, 53242, 810, 2558, 1294, 15402, 94, 550862, 3707, 16658, 680, 2616337, 53, 5701552, 11639, 6606, 30749, 27077004, 800, 21212965, 5215, 611097, 109818, 280237216
OFFSET
0,6
EXAMPLE
a(9) = 5 because we have [7, 2], [5, 2, 2], [2, 7], [2, 5, 2] and [2, 2, 5].
MAPLE
a:= proc(m) option remember; local b; b:= proc(n) option
remember; `if`(n=0, 1, add(`if`(not isprime(j) or
irem(m, j)=0, 0, b(n-j)), j=2..n)) end; b(m)
end:
seq(a(n), n=0..80); # Alois P. Heinz, Mar 11 2018
MATHEMATICA
Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] != 0 && PrimeQ[k]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 53}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 11 2018
STATUS
approved