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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)