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A184999
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Smallest number having exactly n partitions into distinct parts, with each part divisible by the next.
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3
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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
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = min { k : A122651(k) = n }.
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EXAMPLE
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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].
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MAPLE
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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);
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CROSSREFS
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Cf. A122651, A184998.
Sequence in context: A194273 A123581 A187337 * A189783 A189513 A194146
Adjacent sequences: A184996 A184997 A184998 * A185000 A185001 A185002
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Mar 28 2011
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STATUS
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approved
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