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Smallest number with all identical digits having n distinct prime divisors.

3

`%I #7 Dec 05 2013 19:56:21
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`%S 1,2,6,66,6666,111111,222222,111111111111,222222222222,
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`%T 222222222222222222,111111111111111111111111,222222222222222222222222,
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`%U 22222222222222222222222222222222,111111111111111111111111111111
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`%N Smallest number with all identical digits having n distinct prime divisors.
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`%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_
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`%C Sequence could be represented by citing the number of repeated digits concatenated with that digit, e.g., a(8) = 122. See A087450.
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`%e a(6) = 22222222 because the 6 distinct prime divisors of a(6) are 2, 3, 7, 11, 13, and 37.
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`%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}]
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`%K base,nonn
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`%O 1,2
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`%A _Amarnath Murthy_, Sep 05 2003
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`%E Edited, corrected and extended by _Robert G. Wilson v_, Sep 06 2003
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