A062664 Composite and every divisor (except for 1) contains the digit 2.

254, 422, 482, 502, 526, 529, 542, 562, 842, 1042, 1642, 2042, 2246, 2258, 2402, 2426, 2434, 2446, 2458, 2462, 2474, 2498, 2518, 2554, 2558, 2566, 2578, 2582, 2594, 2642, 2654, 2846, 2854, 2858, 2921, 3242, 3254, 3442, 4022, 4126, 4162, 4222, 4226

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Comments

If k is in the sequence, then all composite divisors of k are in the sequence. - Robert Israel, Jul 11 2019

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062649, A062668, A062670, A062672, A062674, A062676, A062678, A062680, A243819.

Programs

Magma

[m:m in [2..4300] | not IsPrime(m) and #[d:d in Divisors(m)|2 in Intseq(d)] eq #Divisors(m)-1]; // Marius A. Burtea, Jul 11 2019

Maple

filter:= proc(n) local D;
  if isprime(n) then return false fi;
  andmap(con2,numtheory:-divisors(n) minus {1})
end proc:
con2:= proc(n) option remember; member(2,convert(n,base,10)) end proc:
select(filter, [$4..10000]);# Robert Israel, Jul 11 2019

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 4230], !PrimeQ[#] && fQ[#, 2] &] (* Robert G. Wilson v, Jun 11 2014 *)

Extensions

Offset changed by Robert Israel, Jul 11 2019