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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A263380 A144855 A110827 * A258696 A158249 A366553

Adjacent sequences: A062661 A062662 A062663 * A062665 A062666 A062667

Keyword

base,easy,nonn

Author

Erich Friedman, Jul 04 2001

Extensions

Offset changed by Robert Israel, Jul 11 2019

Status

approved