A308063 -id:A308063 - cp's OEIS frontend

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

Ilya Gutkovskiy, Sep 25 2022

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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}]

a(1) = 1; a(n) = Sum_{d|n, d < n} A065043(n/d) * a(d).

A357375 Number of ordered factorizations of n into numbers > 1 with an even number of distinct prime divisors.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 3, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 1, 1, 0, 2

Offset: 1

Ilya Gutkovskiy, Sep 25 2022

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A030231, A050334, A074206, A308063, A357374.

f[n_] := Boole[EvenQ[PrimeNu[n]]]; a[1] = 1; a[n_] := a[n] = Sum[If[d < n, f[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]

cp's OEIS Frontend

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

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