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a(n) is the least k such that e(k) = n, where e(k) is the smallest m > 1 such that k^m contains all the digits of k with at least the same multiplicity.
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%I #9 Mar 20 2014 12:03:35

%S 1,4,14,2,15,19,26,118,128,1388,18588,111143,11721111115

%N a(n) is the least k such that e(k) = n, where e(k) is the smallest m > 1 such that k^m contains all the digits of k with at least the same multiplicity.

%C 10^12 < a(15) <= 33333333333338.

%e a(3) = 4 because e(1) = 2 (1^2 = 1), e(2) = 5 (2^5 = 32), e(3) = 5 (3^5 = 243) and finally e(4) = 3 (4^3 = 64).

%t e[k_] := Block[{m=2, d = DigitCount@k}, While[Min[DigitCount[k^m] - d] < 0, m++]; m]; a[n_] := Block[{k=1}, While[e[k] != n, k++]; k]; a /@ Range[2, 11]

%K nonn,base,hard,more

%O 2,2

%A _Giovanni Resta_, Mar 19 2014