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a(n) = n^2 times the squarefree kernel of n.
4

%I #21 Nov 30 2023 02:53:28

%S 1,8,27,32,125,216,343,128,243,1000,1331,864,2197,2744,3375,512,4913,

%T 1944,6859,4000,9261,10648,12167,3456,3125,17576,2187,10976,24389,

%U 27000,29791,2048,35937,39304,42875,7776,50653,54872,59319,16000,68921,74088,79507,42592,30375

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

%H Amiram Eldar, <a href="/A355038/b355038.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = p^(2e+1).

%F a(n) = n^2 * A007947(n).

%F a(n) = A064549(n^2). - _Amiram Eldar_, Jun 20 2022

%F 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 a(n) = A356191(n^2). - _Amiram Eldar_, Nov 30 2023

%t a[n_] := n^2 * Times @@ FactorInteger[n][[;; , 1]]; Array[a, 50] (* _Amiram Eldar_, Jun 18 2022 *)

%o (PARI) a(n) = n^2 * factorback(factor(n)[,1]);

%Y The range of values is A335988.

%Y Cf. A007947, A064549, A065463, A102631, A356191.

%K nonn,easy,mult

%O 1,2

%A _Peter Munn_, Jun 16 2022