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A260906 Numbers n such that 3*n and n^3 have the same digit sum.

%I A260906 #22 Sep 08 2022 08:46:13
%S A260906 0,3,6,30,60,63,126,171,252,300,324,543,585,600,630,1260,1281,1710,
%T A260906 2520,2925,3000,3240,5430,5850,5946,6000,6300,12600,12606,12633,12810,
%U A260906 14631,16263,17100,21618,22308,22971,24663,25200,27633,28845,28887,28965,29241
%N A260906 Numbers n such that 3*n and n^3 have the same digit sum.
%C A260906 All terms are multiples of 3.
%C A260906 n is in the sequence iff 10*n is. Are there infinitely many terms not divisible by 10? - _Robert Israel_, Nov 20 2015
%H A260906 Robert Israel, <a href="/A260906/b260906.txt">Table of n, a(n) for n = 1..320</a>
%F A260906 A007953(A008585(a(n))) = A007953(A000578(a(n))).
%e A260906 126 is in the sequence because 126^3 = 2000376 and 3*126 = 378 have the same digit sum: 18.
%p A260906 select(n -> convert(convert(n^3,base,10),`+`)=convert(convert(3*n,base,10),`+`), 3*[$0..10^5]); # _Robert Israel_, Nov 20 2015
%t A260906 Select[Range[0, 50000], Total[IntegerDigits[3 #]] == Total[IntegerDigits[#^3]] &]
%o A260906 (Magma) [n: n in [0..50000] | &+Intseq(3*n) eq &+Intseq(n^3)];
%o A260906 (PARI) for(n=0, 1e5, if(sumdigits(n^3)==sumdigits(3*n), print1(n, ", "))) \\ _Altug Alkan_, Nov 20 2015
%Y A260906 Cf. A000578, A007953, A008585, A049343, A260702.
%K A260906 nonn,base,easy
%O A260906 1,2
%A A260906 _Vincenzo Librandi_, Nov 18 2015