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A184999 Smallest number having exactly n partitions into distinct parts, with each part divisible by the next. 3
0, 3, 6, 9, 12, 15, 22, 25, 21, 30, 48, 36, 40, 56, 51, 45, 57, 64, 84, 76, 63, 90, 85, 93, 81, 99, 100, 91, 150, 130, 105, 133, 126, 147, 154, 184, 135, 153, 198, 213, 175, 304, 165, 265, 232, 183, 320, 171, 226, 210, 201, 274, 300, 243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = min { k : A122651(k) = n }.

EXAMPLE

a(7) = 22, because A122651(22) = 7 and A122651(m) <> 7 for all m<22.  The 7 partitions of 22 into distinct parts, with each part divisible by the next are: [22], [21,1], [20,2], [18,3,1], [16,4,2], [14,7,1], [12,6,3,1].

MAPLE

with(numtheory):

a:= proc() local t, a, b, bb;

      t:= -1;

      a:= proc() -1 end;

      bb:= proc(n) option remember;

        `if`(n=0, 1, add(bb((n-d)/d), d=divisors(n) minus{1}))

      end:

      b:= n-> `if`(n=0, 1, bb(n)+bb(n-1));

      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=1..100);

MATHEMATICA

b[0]=1; b[n_] := b[n] = Sum[b[(n-d)/d], {d, Divisors[n] // Rest}]; a[0] = 1; a[n_] := For[k=0, True, k++, If[b[k]+b[k-1] == n, Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Dec 03 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A122651, A184998.

Sequence in context: A194273 A123581 A187337 * A289761 A310151 A310152

Adjacent sequences:  A184996 A184997 A184998 * A185000 A185001 A185002

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Mar 28 2011

STATUS

approved

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)