A162822 Positive numbers k such that 36*k/(36-k) are integers.

9, 12, 18, 20, 24, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 45, 48, 52, 54, 60, 63, 72, 84, 90, 108, 117, 144, 180, 198, 252, 360, 468, 684, 1332

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

• nonn
• fini
• full
• easy

Comments

The number k=36 is explicitly included, treating the result of division through zero as an integer.

Row 36 of A191973.

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A191973.

Programs

Maple

for m from 1 to 1332 do if(m=36 or m*36 mod (m-36) = 0)then printf("%d, ", m): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

f[a_,b_]:=(a*b)/(a-b); a=36;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Sort[Join[{36},Select[Range[1500],IntegerQ[(36#)/(36-#)]&]]]  (* Harvey P. Dale, Mar 23 2011 *)

Extensions

Keywords fini,full added by R. J. Mathar, Jul 31 2009