A243819 Composite numbers n such that every divisor of n greater than one contains the digit 0.

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

Author

Barbara W. Waddell and Robert G. Wilson v, Jun 11 2014

Keywords

• nonn
• base
• easy

Examples

			The divisors of 10201 are {1, 101, and 10201}. Except for 1 each has a 0 in its decimal expansion.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Barbara W. Waddell and Robert G. Wilson v)

Crossrefs

Cf. A062649, A062664, A062668, A062670, A062672, A062674, A062676, A062678, A062680.

Programs

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 *)

Extensions

Definition slightly modified by Harvey P. Dale, Aug 15 2024