A325446 The unitary version of Kalmár's function: number of ordered factorizations of n into powers of distinct primes.

1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 3, 1, 1, 3, 1, 3, 3, 3, 1, 3, 1, 3, 1, 3, 1, 13, 1, 1, 3, 3, 3, 3, 1, 3, 3, 3, 1, 13, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 13, 1, 3, 3, 1, 3, 13, 1, 3, 3, 13, 1, 3, 1, 3, 3, 3, 3, 13, 1, 3, 1, 3, 1, 13, 3

Offset

1,6

Links

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

Formula

a(1) = 1 and a(n) = Sum_{d||n} a(d), where d||n are the unitary divisors of n (d such that gcd(d, n/d) = 1).

a(n) = A000670(A001221(n)).

a(n) = A074206(n) for squarefree n (A005117).

Mathematica

f[0] = 1; f[n_] := f[n] = Sum[Binomial[n, k] * f[n - k], {k, 1, n}]; a[n_] := f[PrimeNu[n]]; Array[a, 100]

Crossrefs

Cf. A001221, A000670, A005117, A074206.

Sequence in context: A367482 A367095 A309307 * A337322 A090176 A351544

Adjacent sequences: A325443 A325444 A325445 * A325447 A325448 A325449

Keyword

nonn

Author

Amiram Eldar, Sep 06 2019

Status

approved