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n is divisible by the cube of the number of unitary divisors of n (A034444).
3

%I #8 Aug 05 2019 17:24:03

%S 1,8,16,32,64,128,192,256,320,384,448,512,576,640,704,768,832,896,

%T 1024,1088,1152,1216,1280,1408,1472,1536,1600,1664,1728,1792,1856,

%U 1984,2048,2176,2304,2368,2432,2560,2624,2752,2816,2944,3008,3072,3136,3200,3328

%N n is divisible by the cube of the number of unitary divisors of n (A034444).

%H Amiram Eldar, <a href="/A048169/b048169.txt">Table of n, a(n) for n = 1..10000</a>

%e a[ 54 ]=x=3968=128*31 has 4 unitary divisors: {1,3968,128,31} and the cube, 64, divides 3968: q=3968/64=62.

%t Select[Range[3400], Divisible[#, 8^PrimeNu[#]] &] (* _Amiram Eldar_, Aug 05 2019 *)

%Y A034444, A046755, A048166-A048168.

%K nonn

%O 1,2

%A _Labos Elemer_