A357374 Number of ordered factorizations of n into numbers > 1 with an even number of prime divisors (prime factors counted with multiplicity).

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

Links

Table of n, a(n) for n=1..90.

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}]

Crossrefs

Cf. A028260, A050334, A065043, A074206, A308063, A353337, A357375.

Sequence in context: A193510 A353337 A351907 * A264048 A101257 A321892

Adjacent sequences: A357371 A357372 A357373 * A357375 A357376 A357377

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 25 2022

Status

approved