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%I #15 Nov 13 2022 08:39:28
%S 1,2,3,4,5,6,7,1,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,3,25,26,
%T 1,28,29,30,31,4,33,34,35,36,37,38,39,5,41,42,43,44,45,46,47,48,49,50,
%U 51,52,53,2,55,7,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,9,73,74,75
%N a(n) = n divided by its characteristic cube divisor A056191.
%C Different from A056552: e.g. a(16) = 16, while A056552(16) = 2.
%H Amiram Eldar, <a href="/A056192/b056192.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n/A055229(n)^3 = n/g^3=n/ggg and n=(LL)*(ggg)*f=L^2*g^3*f=LL*a(n)^3*f, so n=L^2*(g*3)*f, where L=A000188(n)/A055229(n), f=A055231(n), g=A055231(n).
%F Multiplicative with a(p^e)=p^e for even e, a(p)=p, a(p^e)=p^(e-3) for odd e>1. - _Vladeta Jovovic_, Apr 30 2002
%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^2/12) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4 + 1/p^6 - 1/p^7) = 0.4462648652... . - _Amiram Eldar_, Nov 13 2022
%t f[p_, e_] := If[EvenQ[e], p^e, If[e == 1, p, p^(e - 3)]]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 06 2020 *)
%Y Cf. A000188, A008833, A007913, A055229, A055231, A056552, A056191.
%K nonn,mult
%O 1,2
%A _Labos Elemer_, Aug 02 2000