A184998 Smallest number having exactly n partitions into distinct parts greater than 1, with each part divisible by the next.

1, 0, 6, 14, 12, 18, 24, 40, 36, 30, 48, 42, 75, 60, 72, 66, 80, 105, 84, 114, 102, 90, 120, 138, 132, 126, 186, 156, 150, 170, 180, 182, 310, 222, 200, 272, 434, 234, 198, 320, 273, 308, 210, 354, 252, 300, 360, 372, 392, 500, 366, 315

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = min { k : A167865(k) = n }.

Example

a(7) = 40, because A167865(40) = 7 and A167865(m) <> 7 for all m<40.  The 7 partitions of 40 into distinct parts greater than 1, with each part divisible by the next are: [40], [38,2], [36,4], [35,5], [32,8], [30,10], [24,12,4].

Maple

with(numtheory):
a:= proc() local t, a, b;
      t:= -1;
      a:= proc() -1 end;
      b:= proc(n) option remember;
            `if`(n=0, 1, add(b((n-d)/d), d=divisors(n) minus{1}))
          end:
      proc(n) local h;
        while a(n) = -1 do
          t:= t+1;
          h:= b(t);
          if a(h) = -1 then a(h):= t fi
        od; a(n)
      end
    end():
seq(a(n), n=0..100);

Mathematica

a[n0_] := Module[{t = -1, a, b}, a[_] = -1; b[n_] := b[n] = If[n == 0, 1, Sum[b[(n - d)/d], {d, Divisors[n] ~Complement~ {1}}]]; While[a[n] == -1, t++; h = b[t]; If[a[h] == -1, a[h] = t]]; a[n0]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Crossrefs

Cf. A167865, A184999.

Sequence in context: A265029 A329065 A338419 * A322561 A079010 A324814

Adjacent sequences: A184995 A184996 A184997 * A184999 A185000 A185001

Keyword

nonn,look

Author

Alois P. Heinz, Mar 28 2011

Status

approved