A384969 Numbers with exactly two distinct base-10 digits that have more divisors than any smaller such number.

10, 12, 24, 36, 48, 60, 144, 252, 336, 600, 900, 2112, 2772, 5544, 9900, 30030, 60060, 144144, 288288, 600600, 900900, 3003000, 6006000, 9009000, 30030000, 33333300, 44444400, 66666600, 90090000, 222222000, 333333000, 666666000, 999999000, 3333330000, 6066660600, 6666660000, 9999990000

Offset

1,1

Comments

Terms k of A031955 such that A000005(k) > A000005(j) for all j < k in A031955.

Links

Robert Israel, Table of n, a(n) for n = 1..58

Example

a(3) = 24 because 24 = A031955(13) has 8 divisors (1,2,3,4,6,8,12, and 24) and A031955(1) to A031955(12) all have fewer than 8 divisors.

Maple

G:= proc(d)
  local S, a, b, s, q, r, i;
  S:= {}:
  for s in combinat:-powerset({$0..d-1}) minus {{}, {$0..d-1}} do
    q:= add(10^i, i=s);
    r:= (10^d-1)/9 - q;
    S:= S union {seq(seq(a*q+b*r, b = a+1..9), a = `if`(q < 10^(d-1), 0, 1) .. 8)};
 od;
S:= sort(convert(S, list));
end proc:
R:= NULL: m:= 0:
for d from 2 to 17 do
  for x in G(d) do
    v:= numtheory:-tau(x);
    if v > m then
       count:= count+1; R:= R, x; m:= v;
    fi
  od
od:
R;

Crossrefs

Cf. A000005, A031955.

Sequence in context: A087697 A241177 A140972 * A108901 A372488 A073083

Adjacent sequences: A384966 A384967 A384968 * A384970 A384971 A384972

Keyword

nonn,base

Author

Robert Israel, Oct 06 2025

Status

approved