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A068187
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a(n) is the smallest number such that the product of its decimal digits equals n^n, or 0 if no solutions exist.
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9
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1, 4, 39, 488, 55555, 88999, 7777777, 88888888, 999999999, 25555555555888, 0, 88888888999999, 0, 4777777777777778888, 35555555555555559999999, 2888888888888888888888, 0, 888888999999999999999999, 0, 2555555555555555555558888888888888, 37777777777777777777779999999999
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OFFSET
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1,2
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COMMENTS
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a(n) = 0 if and only if n has a prime factor > 7. If n > 1 has no prime factor > 7, let n^n = 2^a*3^b*5^c*7^d. Let m(x) denote the number of digit x in a(n). Then a(n) is a number whose digits are nondecreasing and defined as follows. m(2) = 1 if a mod 3 == 1 and 0 otherwise, m(3) = 1 if b mod 2 == 1 and 0 otherwise, m(4) = 1 if a mod 3 == 2 and 0 otherwise, m(5) = c, m(6) = 0, m(7) = d, m(8) = floor(a/3), m(9) = floor(b/2). - Chai Wah Wu, Aug 12 2017
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LINKS
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PROG
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(Python)
from sympy import factorint
if n == 1:
return 1
pf = factorint(n)
return 0 if max(pf) > 7 else int(''.join(sorted(''.join(str(a)*(n*b) for a, b in pf.items()).replace('222', '8').replace('22', '4').replace('33', '9')))) # Chai Wah Wu, Aug 13 2017
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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