A062653 Every divisor (except 1) contains the digit 2.

2, 23, 29, 127, 211, 223, 227, 229, 233, 239, 241, 251, 254, 257, 263, 269, 271, 277, 281, 283, 293, 421, 422, 482, 502, 521, 523, 526, 529, 542, 562, 727, 821, 823, 827, 829, 842, 929, 1021, 1042, 1123, 1129, 1201, 1213, 1217, 1223, 1229, 1231, 1237

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			254 has divisors 1, 2, 127 and 254, all of which contain the digit 2.
		

Links

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

Crossrefs

Cf. A062664, A062667, A062668, A062669, A062670, A062671, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

Magma

[k:k in [2..1300]| forall{d:d in Set(Divisors(k)) diff {1}| 2 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1300], fQ[#, 2] &]  (* Robert G. Wilson v, Jun 11 2014 *)

PARI

has2(n)=if(n==1, return(1)); !!setsearch(Set(digits(n)),2)
is(n)=fordiv(n,d, if(!has2(d), return(0))); 1 \\ Charles R Greathouse IV, Jan 24 2020

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019