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Numbers k that divide (omega(k)*Omega(k))^k.
1

%I #38 Aug 20 2021 05:41:19

%S 1,4,12,16,18,27,64,80,96,144,200,216,256,324,448,486,500,729,768,

%T 1024,1152,1250,1568,1728,2560,2592,3125,3840,3888,4096,5488,5760,

%U 5832,6144,6400,8640,8748,9216,9600,11264,12960,13122,13824,14400,16000,16384

%N Numbers k that divide (omega(k)*Omega(k))^k.

%C This is not a subsequence of A067575: 3840 belongs to this sequence but not to A067575.

%C Also numbers k such that rad(k) = rad(omega(k)*bigomega(k)) where rad is A007947. [_Charles R Greathouse IV_, Jul 18 2011]

%H Arkadiusz Wesolowski, <a href="/A193022/b193022.txt">Table of n, a(n) for n = 1..400</a>

%t Select[Range[12960], PowerMod[PrimeNu[#] PrimeOmega[#], #, #] == 0 &] (* _T. D. Noe_, Jul 14 2011 *)

%o (PARI) for(n=1, 2^14, if(lift(Mod((omega(n)*bigomega(n))^n, n))==0, print1(n, ", "))); \\ _Arkadiusz Wesolowski_, Jul 18 2011

%Y Cf. A001221 (omega), A001222 (Omega), A007947, A067575.

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Jul 14 2011