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A225535 Numbers whose cubed digits sum to a cube, and have more than one nonzero digit.

%I A225535 #27 May 21 2013 04:06:14
%S A225535 168,186,345,354,435,453,534,543,618,681,816,861,1068,1086,1156,1165,
%T A225535 1516,1561,1608,1615,1651,1680,1806,1860,3045,3054,3405,3450,3504,
%U A225535 3540,4035,4053,4305,4350,4503,4530,5034,5043,5116,5161,5304,5340,5403,5430,5611
%N A225535 Numbers whose cubed digits sum to a cube, and have more than one nonzero digit.
%H A225535 Christian N. K. Anderson, <a href="/A225535/b225535.txt">Table of n, a(n) for n = 1..10000</a>
%e A225535 5^3 + 6^3 + 1^3 + 1^3 = 343, which is 7^3.
%t A225535 fQ[n_] := Module[{d = IntegerDigits[n]}, Count[d, 0] + 1 < Length[d] && IntegerQ[Total[d^3]^(1/3)]]; Select[Range[5611], fQ] (* _T. D. Noe_, May 19 2013 *)
%o A225535 (R)y=rep(0,10000); len=0; x=0; library(gmp);
%o A225535 digcubesum<-function(x) sum(as.numeric(unlist(strsplit(as.character(as.bigz(x)),split="")))^3);
%o A225535 iscube<-function(x) ifelse(as.bigz(x)<2,T,all(table(as.numeric(factorize(x)))%%3==0));
%o A225535 nonzerodig<-function(x) sum(strsplit(as.character(x),split="")[[1]]!="0");
%o A225535 which(sapply(1:6000,function(x) nonzerodig(x)>1 & iscube(digcubesum(x))))
%Y A225535 Cf. A225534 (cubed digits sum to a prime), A197039 (square), A046459. A055012.
%Y A225535 Cf. A165330 (cube cycle), A046197 (cubic fixed points), A000578 (cubes).
%Y A225535 Cf. A052034 (squared digits sum to a prime), A028839, A117685.
%Y A225535 Cf. A164882 (n such that sum of the cubes of the digits of n^3 is perfect cube). - _Zak Seidov_, May 21 2013
%K A225535 nonn,base
%O A225535 1,1
%A A225535 _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 10 2013