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%I
%S 1,2,6,66,6666,111111,222222,111111111111,222222222222,
%T 222222222222222222,111111111111111111111111,222222222222222222222222,
%U 22222222222222222222222222222222,111111111111111111111111111111
%N Smallest number with all identical digits having n distinct prime divisors.
%C The conjecture that 'for n > 2, a(n) == 0 (mod 3)' is not true since a(12) = 32 2's which is == 1 (mod 3). - Robert G. Wilson v.
%C Sequence could be represented by citing the number of repeated digits concatenated with that digit, e.g. a(8) = 122. See A087450.
%e a(6) = 22222222 because the 6 distinct prime divisors of a(6) are 2,3,7,11,13&37.
%t PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; Do[k = 1; While[t = Table[j*(10^k - 1)/9, {j, 1, 9}]; l = Map[ Length, Map[ PrimeFactors, t]]; Position[l, n] == {}, k++ ]; Print[ t[[Position[l, n] [[1, 1]]]]], {n, 0, 13}]
%K base,nonn
%O 1,2
%A Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 05 2003
%E Edited, corrected and extended by _Robert G. Wilson v_, Sept 06 2003
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