A062678 - OEIS

A062678

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

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

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A345149 A345603 A345862 * A018848 A031581 A031761

Adjacent sequences: A062675 A062676 A062677 * A062679 A062680 A062681

KEYWORD

base,easy,nonn

AUTHOR

Erich Friedman, Jul 04 2001

EXTENSIONS

Offset corrected by Amiram Eldar, Nov 07 2019

STATUS

approved