A062668 Composite and every divisor (except 1) contains the digit 3.

39, 93, 309, 339, 393, 403, 713, 933, 939, 993, 1137, 1293, 1317, 1329, 1333, 1339, 1369, 1389, 1643, 1703, 1839, 1893, 2263, 2319, 2369, 2573, 3013, 3029, 3039, 3071, 3093, 3099, 3107, 3117, 3139, 3151, 3189, 3193, 3197, 3279, 3309, 3369, 3419, 3459

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			93 has divisors 1, 3, 31 and 93, all of which contain the digit 3.
		

Links

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

Crossrefs

Cf. A062653, A062664, A062667, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

Magma

[k:k in [2..3500]| forall{d:d in Set(Divisors(k)) diff {1}| 3 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 3460], !PrimeQ[#] && fQ[#, 3] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019