A192034 Least k such that (product of proper divisors of k) mod (sum of proper divisors of k) equals n.

2, 8, 4, 9, 14, 25, 15, 49, 22, 18, 21, 57, 45, 169, 34, 69, 38, 205, 143, 119, 46, 87, 217, 93, 130, 133, 58, 323, 62, 111, 160, 553, 319, 63, 74, 129, 30, 305, 82, 75, 86, 36, 68, 335, 48, 159, 301, 355, 369, 171, 106, 177

Offset: 0

Author

Juri-Stepan Gerasimov, Jun 21 2011

Keywords

• nonn

Comments

Greedy inverse of A191906.

Examples

			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;
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;
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.
		

Crossrefs

Cf. A001065, A007956, A191906.

Programs

Maple

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

Mathematica

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 *)

Extensions

Corrected by R. J. Mathar, Jul 01 2011

Example section corrected by Jon E. Schoenfield, Feb 24 2019