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%I #13 Feb 24 2019 12:33:20
%S 2,8,4,9,14,25,15,49,22,18,21,57,45,169,34,69,38,205,143,119,46,87,
%T 217,93,130,133,58,323,62,111,160,553,319,63,74,129,30,305,82,75,86,
%U 36,68,335,48,159,301,355,369,171,106,177
%N Least k such that (product of proper divisors of k) mod (sum of proper divisors of k) equals n.
%C Greedy inverse of A191906.
%e a(0)=2 because A007956(2) mod A001065(2) = 1 mod 1 = 0, and 2 is the smallest number for which this is the case;
%e a(1)=8 because A007956(8) mod A001065(8) = 8 mod 7 = 1, and 8 is the smallest number for which this is the case;
%e a(2)=4 because A007956(4) mod A001065(4) = 2 mod 3 = 2, and 4 is the smallest number for which this is the case.
%p A192034 := proc(n) local k ; for k from 2 do if A191906(k) = n then return k ; end if; end do: end proc: # _R. J. Mathar_, Jul 01 2011
%t ds[n_]:=Module[{divs=Most[Divisors[n]]},Mod[Times@@divs,Total[divs]]]; Join[ {2},Transpose[Table[SelectFirst[Table[{n,ds[n]},{n,2,2000}],#[[2]] == i&],{i,60}]][[1]]] (* _Harvey P. Dale_, Apr 11 2015 *)
%Y Cf. A001065, A007956, A191906.
%K nonn
%O 0,1
%A _Juri-Stepan Gerasimov_, Jun 21 2011
%E Corrected by _R. J. Mathar_, Jul 01 2011
%E Example section corrected by _Jon E. Schoenfield_, Feb 24 2019
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