

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
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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((nd)/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}] (* JeanFrançois Alcover, May 21 2018, translated from Maple *)


CROSSREFS

Cf. A167865, A184999.
Sequence in context: A131902 A265029 A329065 * A322561 A079010 A324814
Adjacent sequences: A184995 A184996 A184997 * A184999 A185000 A185001


KEYWORD

nonn,look


AUTHOR

Alois P. Heinz, Mar 28 2011


STATUS

approved



