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A184998 Smallest number having exactly n partitions into distinct parts greater than 1, with each part divisible by the next. 3

%I

%S 1,0,6,14,12,18,24,40,36,30,48,42,75,60,72,66,80,105,84,114,102,90,

%T 120,138,132,126,186,156,150,170,180,182,310,222,200,272,434,234,198,

%U 320,273,308,210,354,252,300,360,372,392,500,366,315

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

%H Alois P. Heinz, <a href="/A184998/b184998.txt">Table of n, a(n) for n = 0..10000</a>

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

%e 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].

%p with(numtheory):

%p a:= proc() local t, a, b;

%p t:= -1;

%p a:= proc() -1 end;

%p b:= proc(n) option remember;

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

%p end:

%p proc(n) local h;

%p while a(n) = -1 do

%p t:= t+1;

%p h:= b(t);

%p if a(h) = -1 then a(h):= t fi

%p od; a(n)

%p end

%p end():

%p seq(a(n), n=0..100);

%t 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]];

%t Table[a[n], {n, 0, 100}] (* _Jean-Fran├žois Alcover_, May 21 2018, translated from Maple *)

%Y Cf. A167865, A184999.

%K nonn,look

%O 0,3

%A _Alois P. Heinz_, Mar 28 2011

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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)