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A357374
Number of ordered factorizations of n into numbers > 1 with an even number of prime divisors (prime factors counted with multiplicity).
1
1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1, 1, 0, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 4, 0, 1, 1, 3, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 3, 1, 3, 1, 1, 0, 5, 0, 1, 0, 4, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 5, 1, 1, 1, 3, 0, 5
OFFSET
1,16
FORMULA
a(1) = 1; a(n) = Sum_{d|n, d < n} A065043(n/d) * a(d).
MATHEMATICA
A065043[n_] := Boole[EvenQ[PrimeOmega[n]]]; a[1] = 1; a[n_] := a[n] = Sum[If[d < n, A065043[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2022
STATUS
approved