

A086146


a(n) is the smallest k>=n such that the number of partitions of k is a multiple of n, or 1 if no such k exists.


1



1, 2, 3, 11, 7, 9, 10, 11, 14, 19, 12, 21, 28, 19, 24, 66, 54, 21, 20, 58, 24, 25, 32, 70, 44, 28, 39, 55, 91, 97, 44, 66, 35, 94, 39, 80, 86, 47, 129, 66, 45, 75, 100, 58, 129, 75, 56, 70, 68, 74, 178, 62, 66, 340, 58, 75, 209, 97, 93, 124, 115, 101, 138, 66, 84, 75, 111, 94
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OFFSET

1,2


COMMENTS

I do not know if a(n) exists for all n. First term which is currently unknown is a(2219) (a(2219) > 11600, while a(2218) = 2602).


LINKS

Table of n, a(n) for n=1..68.


EXAMPLE

a(4) is 11 because 11 is the smallest number for which P(11) is divisible by 4, where P() is the partition function.


MAPLE

for i from 2 while i < 30000 do for j from i while j < 1000000000 do c := numbpart(j); if (c mod i = 0) then print(i, j); break; end if; end do; end do;
# alternative
A086146 := proc(n)
local k ;
for k from n do
if combinat[numbpart](k) mod n =0 then
return k;
end if;
end do:
end proc: # R. J. Mathar, Apr 22 2013


CROSSREFS

Cf. A046641.
Sequence in context: A282770 A145077 A127376 * A083758 A127494 A320264
Adjacent sequences: A086143 A086144 A086145 * A086147 A086148 A086149


KEYWORD

nonn


AUTHOR

Jim Nastos, Aug 25 2003


EXTENSIONS

More terms from Ray Chandler, Sep 16 2003


STATUS

approved



