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Odd numbers whose set of prime factors (taken with multiplicity) uses each digit from 0 to 9 exactly once.
1

%I #12 Dec 19 2014 18:54:34

%S 42279945,42315045,42514845,43092645,43767645,45981645,46149045,

%T 46321845,52226745,52654695,53159595,56789745,56841045,57321645,

%U 58193745,59869345,61277145,61421595,61860445,62146545,62866645,62936295,62969845,63395295,63411595

%N Odd numbers whose set of prime factors (taken with multiplicity) uses each digit from 0 to 9 exactly once.

%C This sequence also contains numbers not ending in 5 (i.e., 78369189).

%C a(1916) = 240510701 is the first semiprime with this property.

%C No pandigital number is in the sequence.

%H Arkadiusz Wesolowski, <a href="/A213737/b213737.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_factor">Prime factor</a>

%e 42279945 = 3*5*1049*2687 is in the sequence since the set {3, 5, 1049, 2687} can be formed from the digits 0 to 9 and each digit is used only once.

%t lst = {}; Do[If[Equal[Sort@Flatten@IntegerDigits@FactorInteger[n][[All, {1}]], {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}] && SquareFreeQ[n], AppendTo[lst, n]], {n, 4*10^7 + 1, 7*10^7, 2}]; lst

%t ed1Q[n_]:=Module[{fi=FactorInteger[n]},Max[Transpose[fi][[2]]]==1 && Union[ Flatten[IntegerDigits/@Transpose[fi][[1]]]]==Range[0,9]]; Select[Range[ 4*10^7+ 1,6.4*10^7,2 ],ed1Q] (* _Harvey P. Dale_, Dec 19 2014 *)

%Y Subsequence of A058909.

%K base,fini,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Jun 19 2012