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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
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
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
Sequence in context: A265029 A329065 A338419 * A322561 A079010 A324814
KEYWORD
nonn,look
AUTHOR
Alois P. Heinz, Mar 28 2011
STATUS
approved