A Sequence With Only Eight Members

The idea popped into my head to look for numbers that together with their prime factors contain all the digits exactly once. This proved to be a relatively straight forward exercise. Up to one million, there are only eight numbers that qualify. These numbers together with their factorisations are as follows (permalink):

• \(10968 = 2^3 \times 3 \times 457 \)
  
• \(28651 = 7 \times 4093 \)
  
• \(43610 = 2 \times 5 \times 7^2 \times 89 \)
  
• \(48960 = 2^6 \times 3^2 \times 5 \times 17 \)
  
• \(50841 = 3^3 \times 7 \times 269 \)
  
• \(65821 = 7 \times 9403 \)
  
• \(80416 = 2^5 \times 7 \times 359 \)
  
• \(90584 = 2^3 \times 13^2 \times 67 \)

If repeated prime factors are disallowed, then only \(28651\) and \(65821\) qualify. These eight numbers, as I subsequently discovered, make up OEIS A124668:

A124668

Numbers that together with their prime factors contain every digit exactly once.

So this is the sequence with only eight members: 10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584.