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A086146
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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.
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1
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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
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1,2
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COMMENTS
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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).
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LINKS
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EXAMPLE
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a(4) is 11 because 11 is the smallest number for which P(11) is divisible by 4, where P() is the partition function.
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MAPLE
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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
local k ;
for k from n do
if combinat[numbpart](k) mod n =0 then
return k;
end if;
end do:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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