A385351 Perfect powers whose digits are all powers of the same single-digit base.
1, 4, 8, 9, 16, 81, 121, 128, 144, 441, 484, 841, 1331, 1444, 8281, 11881, 14884, 28224, 48841, 114244, 128881, 142884, 221841, 228484, 848241, 1121481, 1281424, 1418481, 2184484, 2214144, 8282884, 9393931, 11142244, 11282881, 18241441, 18818244, 18844281, 21242881
Offset: 1
Examples
841 is a term since it is equal to 29^2 and its digits are all powers of 2: 8 = 2^3, 4 = 2^2, and 1 = 2^0; 1331 is a term since it is equal to 11^3 and its digits are all powers of 3: 1 = 3^0 and 3 = 3^1.
Programs
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Mathematica
perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) nterms=20; list={}; len=0; n=1; While[len <=nterms, If[perfectPowerQ[n] &&(SubsetQ[{0}, dig=IntegerDigits[n]] || SubsetQ[{1, 2, 4, 8}, dig] || SubsetQ[{1, 3, 9}, dig] || SubsetQ[{1, 5}, dig] || SubsetQ[{1, 6}, dig] || SubsetQ[{1, 7}, dig]),AppendTo[list,n]; len++]; n++]; list