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Powerful(1) numbers (A001694) whose digit reversal is a cube.
3

%I #15 Feb 24 2024 11:04:35

%S 1,8,72,100,343,800,1000,1331,7200,8000,10000,34300,72000,80000,

%T 100000,133100,343000,720000,800000,1000000,1030301,1331000,1367631,

%U 3430000,7200000,8000000,10000000,13310000,34300000,72000000,80000000,100000000,103030100,133100000

%N Powerful(1) numbers (A001694) whose digit reversal is a cube.

%H Amiram Eldar, <a href="/A115693/b115693.txt">Table of n, a(n) for n = 1..180</a>

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.

%e 72 = 2^3*3^2 is powerful and 27 = 3^3.

%t Select[Join[{1},Select[Range[10000000],Min[Transpose[ FactorInteger[#]] [[2]]]>1&]],IntegerQ[Power[FromDigits[Reverse[IntegerDigits[#]]], (3)^-1]]&] (* _Harvey P. Dale_, Sep 18 2011 *)

%Y Cf. A001694, A115694.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, Jan 31 2006

%E a(28)-a(34) from _Amiram Eldar_, Feb 24 2024