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A345390
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Numbers whose set of divisors contains every digit at least twice.
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2
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540, 720, 760, 810, 918, 1080, 1140, 1170, 1260, 1404, 1440, 1512, 1520, 1530, 1560, 1620, 1740, 1800, 1820, 1824, 1836, 1872, 1890, 1908, 1960, 2016, 2028, 2052, 2070, 2072, 2088, 2106, 2112, 2124, 2142, 2156, 2160, 2184, 2208, 2280, 2340, 2380, 2430, 2508, 2520
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OFFSET
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1,1
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COMMENTS
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Compare to A095050: Numbers such that all ten digits are needed to write all positive divisors in decimal representation.
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LINKS
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EXAMPLE
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The divisors of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, and 918. Every digit appears at least twice. Thus, 918 is in this sequence.
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MAPLE
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q:= n-> (p-> is(min(seq(coeff(p, x, j), j=0..9))>1))(add(x^i, i=
map(d-> convert(d, base, 10)[], [numtheory[divisors](n)[]]))):
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MATHEMATICA
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Select[Range[3000], Length[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] == 10 && Min[Transpose[Tally[Flatten[IntegerDigits[Divisors[#]]]]][[2]]] > 1 &]
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PROG
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(Python)
from sympy import divisors
def ok(n):
digits_used = {d:0 for d in "0123456789"}
for div in divisors(n, generator=True):
for d in str(div): digits_used[d] += 1
if all(digits_used[d] > 1 for d in "0123456789"): return True
return False
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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