

A062664


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


18



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
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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 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 A255178
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



