cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A359594 #19 Nov 22 2023 10:47:33
%S A359594 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,
%T A359594 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,
%U A359594 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
%N A359594 Multiplicative with a(p^e) = p^e if p divides e, 1 otherwise.
%C A359594 Each term a(n) divides both A085731(n) and A327939(n).
%H A359594 Antti Karttunen, <a href="/A359594/b359594.txt">Table of n, a(n) for n = 1..16384</a>
%F A359594 a(n) = n / A359593(n).
%t A359594 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 *)
%o A359594 (PARI) A359594(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 1]^(f[k,2]*!(f[k, 2]%f[k, 1]))); };
%o A359594 (Python)
%o A359594 from math import prod
%o A359594 from sympy import factorint
%o A359594 def A359594(n): return prod(p**e for p, e in factorint(n).items() if not e%p) # _Chai Wah Wu_, Jan 10 2023
%Y A359594 Cf. A359593.
%Y A359594 Cf. also A085731, A327939.
%K A359594 nonn,mult
%O A359594 1,4
%A A359594 _Antti Karttunen_, Jan 09 2023