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A062678 Composite and every divisor (except 1) contains the digit 8. 18

%I #25 Sep 08 2022 08:45:03

%S 6889,7387,23489,25187,31789,32287,34087,48721,50861,56689,60787,

%T 68143,68309,68641,68807,73289,73781,76807,78053,78409,78587,78943,

%U 78961,80089,81589,87487,88147,98023,98521,106489,106987,108389,110087

%N Composite and every divisor (except 1) contains the digit 8.

%H Amiram Eldar, <a href="/A062678/b062678.txt">Table of n, a(n) for n = 1..10000</a>

%e 7387 has divisors 83, 89 and 7387, each of which contains the digit 8.

%t 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 *)

%t 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 *)

%o (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

%Y Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062679, A062680.

%K base,easy,nonn

%O 1,1

%A _Erich Friedman_, Jul 04 2001

%E Offset corrected by _Amiram Eldar_, Nov 07 2019

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)