A087331 Smallest number with all identical digits having n distinct prime divisors.

1, 2, 6, 66, 6666, 111111, 222222, 111111111111, 222222222222, 222222222222222222, 111111111111111111111111, 222222222222222222222222, 22222222222222222222222222222222, 111111111111111111111111111111

Offset: 1

Author

Amarnath Murthy, Sep 05 2003

Keywords

• base
• nonn

Comments

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

Sequence could be represented by citing the number of repeated digits concatenated with that digit, e.g., a(8) = 122. See A087450.

Examples

			a(6) = 22222222 because the 6 distinct prime divisors of a(6) are 2, 3, 7, 11, 13, and 37.
		

Programs

Mathematica

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}]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Sep 06 2003