A359594 Multiplicative with a(p^e) = p^e if p divides e, 1 otherwise.

1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 27, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 27, 1, 1, 1, 1, 1, 4, 1, 1, 1, 64, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 108

Offset

1,4

Comments

Each term a(n) divides both A085731(n) and A327939(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = n / A359593(n).

Mathematica

f[p_, e_] := If[Divisible[e, p], p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 09 2023 *)

Prog

(PARI) A359594(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 1]^(f[k, 2]*!(f[k, 2]%f[k, 1]))); };
(Python)
from math import prod
from sympy import factorint
def A359594(n): return prod(p**e for p, e in factorint(n).items() if not e%p) # Chai Wah Wu, Jan 10 2023

Crossrefs

Cf. A359593.

Cf. also A085731, A327939.

Sequence in context: A370703 A365487 A368172 * A368331 A366145 A204160

Adjacent sequences: A359591 A359592 A359593 * A359595 A359596 A359597

Keyword

nonn,mult

Author

Antti Karttunen, Jan 09 2023

Status

approved