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A066736
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Least number > 1 such that the nonzero product of the digits of its n-th power is also an n-th power.
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0
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OFFSET
| 1,1
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COMMENTS
| The n-th roots of the product of the digits of the n-th power of a(n) are 2, 2, 2, 42, 24, 1440, 2520, 6, 10080. Because the numbers get larger quicker, the available candidates decreases. See A020665. Therefore this sequence might be finite or have a preponderance of blank entries. If a(10) exists it > 2*10^7.
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EXAMPLE
| a(5) = 382 because no number less than 382 and 382^5 = 8134236862432, the product of these digits = 7962624 = 24^5.
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MATHEMATICA
| Do[k = 2; While[a = Apply[Times, IntegerDigits[k^n]]; a == 0 || !IntegerQ[a^(1/n)], k++ ]; Print[k], {n, 1, 10} ]
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CROSSREFS
| Sequence in context: A045983 A102384 A125838 * A057330 A186069 A079243
Adjacent sequences: A066733 A066734 A066735 * A066737 A066738 A066739
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KEYWORD
| nonn,base
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 15 2002
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