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A062678
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Composite and every divisor (except 1) contains the digit 8.
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18
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6889, 7387, 23489, 25187, 31789, 32287, 34087, 48721, 50861, 56689, 60787, 68143, 68309, 68641, 68807, 73289, 73781, 76807, 78053, 78409, 78587, 78943, 78961, 80089, 81589, 87487, 88147, 98023, 98521, 106489, 106987, 108389, 110087
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OFFSET
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1,1
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LINKS
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EXAMPLE
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7387 has divisors 83, 89 and 7387, each of which contains the digit 8.
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MATHEMATICA
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fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 110100], !PrimeQ[#] && fQ[#, 8] &] (* Robert G. Wilson v, Jun 11 2014 *)
dc8Q[n_]:=AllTrue[Rest[Divisors[n]], DigitCount[#, 10, 8]>0&]; Select[Range[ 111000], CompositeQ[#]&&dc8Q[#]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2020 *)
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PROG
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(Magma) [k:k in [2..120000]| not IsPrime(k) and forall{d:d in Set(Divisors(k)) diff {1}| 8 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019
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CROSSREFS
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Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062679, A062680.
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KEYWORD
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base,easy,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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