This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227072 #17 Sep 06 2013 00:10:59
%S A227072 1,12,22,123,333,1224,1234,2244,4444,12235,12345,33336,33346,55555,
%T A227072 111225,111445,112455,114555,122346,122446,123456,144466,222226,
%U A227072 224466,244557,244666,333357,333666,345567,355567,455667,666666,1122556,1134457,1145557,1155666
%N A227072 Positive numbers with nondecreasing digits such that sum of cubes of the digits equals the square of the sum of the digits.
%C A227072 Because the digits are nondecreasing, the search to 10^20 is fairly rapid.
%H A227072 T. D. Noe, <a href="/A227072/b227072.txt">Table of n, a(n) for n = 1..660</a>
%e A227072 1234 is here because 1^3 + 2^3 + 3^3 + 4^3 = (1 + 2 + 3 + 4)^2 and its digits are nondecreasing..
%t A227072 (* complete sequence *) tx = {}; Do[d = {i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20}; If[Total[d^3] == Total[d]^2, n = FromDigits[d]; AppendTo[tx, n]], {i1, 0, 9}, {i2, i1, 9}, {i3, i2, 9}, {i4, i3, 9}, {i5, i4, 9}, {i6, i5, 9}, {i7, i6, 9}, {i8, i7, 9}, {i9, i8, 9}, {i10, i9, 9}, {i11, i10, 9}, {i12, i11, 9}, {i13, i12, 9}, {i14, i13, 9}, {i15, i14, 9}, {i16, i15, 9}, {i17, i16, 9}, {i18, i17, 9}, {i19, i18, 9}, {i20, i19, 9}]; tx = Rest[tx]
%t A227072 (* partial sequence *) nddQ[n_] := Module[{idn=IntegerDigits[n]}, Min[Differences[idn]] >= 0 && Total[idn^3] == Total[idn]^2]; Select[Range[2000000], nddQ] (* _Harvey P. Dale_, Sep 01 2013 *)
%Y A227072 Cf. A225567 (primes in a related sequence), A227073.
%K A227072 nonn,base,fini,full
%O A227072 1,2
%A A227072 _T. D. Noe_, Jul 27 2013