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Squarefree kernels of nonsquarefree numbers.
3

%I #15 Dec 09 2023 07:06:58

%S 2,2,3,6,2,6,10,6,5,3,14,2,6,10,22,15,6,7,10,26,6,14,30,21,2,34,6,15,

%T 38,10,3,42,22,30,46,6,14,33,10,26,6,14,58,39,30,11,62,5,42,2,66,15,

%U 34,70,6,21,74,30,38,51,78,10,6,82,42,13,57,86,35,22,30,46,94,21,6,14,66

%N Squarefree kernels of nonsquarefree numbers.

%H Amiram Eldar, <a href="/A076333/b076333.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007947(A013929(n)).

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = (A065463 - 6/Pi^2)/(1 - 6/Pi^2)^2 = 0.627858264532... . - _Amiram Eldar_, Dec 09 2023

%t f[n_] := If[(r = Times @@ FactorInteger[n][[;; , 1]]) < n, r , 0]; Select[f /@ Range[200], # > 0 &] (* _Amiram Eldar_, Sep 07 2020 *)

%Y Cf. A007947, A013929.

%Y Cf. A059956, A065463.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 06 2002