A392961 Numbers k that are the concatenation of two divisors of k.

11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99, 110, 120, 125, 150, 210, 220, 240, 250, 312, 315, 330, 360, 375, 416, 420, 440, 480, 510, 520, 525, 550, 612, 624, 630, 660, 714, 728, 735, 770, 816, 832, 840, 880, 918, 936, 945, 990, 1010, 1020, 1040, 1050, 1100, 1111, 1122, 1125, 1144

Offset

1,1

Comments

In contrast to A249766, leading zeros are not allowed.

Numbers of the form a*10^m + a*b where m >= 1, 10^(m-1) <= a*b < 10^m and b divides 10^m.

Links

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

Example

a(5) = 24 is a term because 24 is the concatenation of 2 and 4, which are both divisors of 24.

Maple

N:= 10^4: # for terms <= N
R:= {}:
for a from 1 to floor(sqrt(N)) do
  for m from 1 to 1+ilog10(N) do
    for b in NumberTheory:-Divisors(10^m) do
      if a*b >= 10^(m-1) and a*b < 10^m and a*(10^m+b) <= N then
         R:= R union {a*(10^m+b)}
      fi
od od od:
sort(convert(R, list));

Mathematica

f[{a_, b_}]:=FromDigits[Flatten[IntegerDigits/@{a, b}]]; q[k_]:=ContainsAny[f/@Permutations[Flatten[Table[Drop[Divisors[k], -1], 2]], {2}], {k}]; Select[Range[1144], q] (* James C. McMahon, Apr 17 2026 *)

Crossrefs

Cf. A249766, A395128, A395129.

Sequence in context: A292683 A139138 A249766 * A113600 A255725 A287442

Adjacent sequences: A392958 A392959 A392960 * A392962 A392963 A392964

Keyword

nonn,base

Author

Robert Israel, Apr 09 2026

Status

approved