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=23×3×457
- 28651=7×4093
- 43610=2×5×72×89
- 48960=26×32×5×17
- 50841=33×7×269
- 65821=7×9403
- 80416=25×7×359
- 90584=23×132×67
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.
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