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
Links
- Antti Karttunen, Table of n, a(n) for n = 1..16384
Programs
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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 *)
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PARI
A359594(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 1]^(f[k,2]*!(f[k, 2]%f[k, 1]))); };
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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
Formula
a(n) = n / A359593(n).
Comments