A213737 Odd numbers whose set of prime factors (taken with multiplicity) uses each digit from 0 to 9 exactly once.

42279945, 42315045, 42514845, 43092645, 43767645, 45981645, 46149045, 46321845, 52226745, 52654695, 53159595, 56789745, 56841045, 57321645, 58193745, 59869345, 61277145, 61421595, 61860445, 62146545, 62866645, 62936295, 62969845, 63395295, 63411595

Offset

1,1

Comments

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

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

No pandigital number is in the sequence.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Wikipedia, Prime factor

Example

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.

Mathematica

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
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 *)

Crossrefs

Subsequence of A058909.

Sequence in context: A198168 A218109 A263561 * A254091 A254098 A276714

Adjacent sequences: A213734 A213735 A213736 * A213738 A213739 A213740

Keyword

base,fini,nonn

Author

Arkadiusz Wesolowski, Jun 19 2012

Status

approved