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).

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

MATHEMATICA

kmax = 10^9;

a[n_] := Module[{k}, For[k = n, k <= kmax, k++, If[Divisible[ PartitionsP[k], n], Return[k]]]] /. Null -> -1;

Table[a[n], {n, 1, 68}] (* Jean-François Alcover, Jul 08 2024 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

Jim Nastos, Aug 25 2003

EXTENSIONS

More terms from Ray Chandler, Sep 16 2003

STATUS

approved