A243819 -id:A243819 - cp's OEIS frontend

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

Erich Friedman, Jul 04 2001

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

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

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

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

[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

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

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 *)

Offset changed by Robert Israel, Jul 11 2019

A243825 Numbers n such that every divisor greater than 1 contains the digit 0.

Original entry on oeis.org

101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1201, 1301, 1303, 1307, 1409, 1601, 1607, 1609, 1709, 1801, 1901, 1907, 2003, 2011, 2017, 2027, 2029

Offset: 1

Barbara W. Waddell and Robert G. Wilson v, Jun 11 2014

This is an example of a composite number in the sequence which demonstrates that A056709 is a proper subsequence. - R. J. Mathar, Jun 13 2014

			The divisors of 10201 are {1, 101 & 10201}. Except for 1 each has a 0 in its decimal expansion.

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

Cf. A062634, A062653, A062667, A062669, A062671, A062673, A062675, A062677, A062679.

Supersequence of A056709 (primes) and A243819 (composites).

[m:m in [2..2100] |  #[d:d in Divisors(m)|0 in Intseq(d)] eq #Divisors(m)-1]; // Marius A. Burtea, Nov 08 2019

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 2030], fQ[#, 0] &]

cp's OEIS Frontend

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

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