A062680 Composite numbers whose divisors (except 1) all contain the digit 9.

1691, 2291, 3629, 5191, 5539, 5597, 6931, 7391, 7921, 7961, 8497, 8791, 9101, 9329, 9409, 9481, 9671, 9701, 10981, 10991, 11269, 13129, 13891, 14239, 15089, 15931, 15941, 16999, 17197, 17309, 17879, 17951, 17993, 18091, 18449, 18829, 18943

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			7961 has divisors 19, 419 and 7961, all of which contain the digit 9.
		

Links

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

Crossrefs

Composite members of A062679.

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678.

Programs

Magma

[k:k in [2..20000]|  not IsPrime(k) and forall{d:d in Set(Divisors(k)) diff {1}| 9 in Intseq(d)}];// Marius A. Burtea, Nov 07 2019

Mathematica

fQ[n_] := Union[Drop[Last /@ Sort /@ IntegerDigits[ Divisors[ n]], 1]] == {9}; Select[ Range[ 19110], fQ[ # ] == True && ! PrimeQ[ # ] &] (* Zak Seidov and Robert G. Wilson v, May 17 2005 *)
fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 19110], !PrimeQ[#] && fQ[#, 9] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 16 2007