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A243819
Composite numbers n such that every divisor of n greater than one contains the digit 0.
3
10201, 10403, 10609, 10807, 11009, 11021, 31007, 40501, 41303, 41309, 42907, 43709, 50803, 51409, 51809, 60701, 61307, 61903, 64307, 65509, 70801, 71609, 72203, 73027, 75007, 76409, 81709, 91607, 97049, 101909, 102313, 102919, 103121, 103927, 104131, 104333, 104339, 104939, 104957, 105163, 105949
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Barbara W. Waddell and Robert G. Wilson v)
EXAMPLE
The divisors of 10201 are {1, 101, and 10201}. Except for 1 each has a 0 in its decimal expansion.
MATHEMATICA
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 106000], !PrimeQ[#] && fQ[#, 0] &]
cd0Q[n_]:=CompositeQ[n]&&AllTrue[Rest[Divisors[n]], DigitCount[#, 10, 0]>0&]; Select[Range[ 106000], cd0Q] (* Harvey P. Dale, Aug 15 2024 *)
KEYWORD
nonn,base,easy
AUTHOR
Barbara W. Waddell and Robert G. Wilson v, Jun 11 2014
EXTENSIONS
Definition slightly modified by Harvey P. Dale, Aug 15 2024
STATUS
approved