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.

A355038 a(n) = n^2 times the squarefree kernel of n.

This page as a plain text file.
%I A355038 #21 Nov 30 2023 02:53:28
%S A355038 1,8,27,32,125,216,343,128,243,1000,1331,864,2197,2744,3375,512,4913,
%T A355038 1944,6859,4000,9261,10648,12167,3456,3125,17576,2187,10976,24389,
%U A355038 27000,29791,2048,35937,39304,42875,7776,50653,54872,59319,16000,68921,74088,79507,42592,30375
%N A355038 a(n) = n^2 times the squarefree kernel of n.
%H A355038 Amiram Eldar, <a href="/A355038/b355038.txt">Table of n, a(n) for n = 1..10000</a>
%F A355038 Multiplicative with a(p^e) = p^(2e+1).
%F A355038 a(n) = n^2 * A007947(n).
%F A355038 a(n) = A064549(n^2). - _Amiram Eldar_, Jun 20 2022
%F A355038 Sum_{k=1..n} a(k) ~ c * n^4, where c = (1/4) * Product_{p prime} (1 - 1/(p*(p+1))) = A065463 / 4 = 0.1761105502... . - _Amiram Eldar_, Nov 13 2022
%F A355038 a(n) = A356191(n^2). - _Amiram Eldar_, Nov 30 2023
%t A355038 a[n_] := n^2 * Times @@ FactorInteger[n][[;; , 1]]; Array[a, 50] (* _Amiram Eldar_, Jun 18 2022 *)
%o A355038 (PARI) a(n) = n^2 * factorback(factor(n)[,1]);
%Y A355038 The range of values is A335988.
%Y A355038 Cf. A007947, A064549, A065463, A102631, A356191.
%K A355038 nonn,easy,mult
%O A355038 1,2
%A A355038 _Peter Munn_, Jun 16 2022