A162823 Positive numbers k such that 42*k/(42-k) are integers.

6, 14, 21, 24, 28, 30, 33, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 51, 54, 56, 60, 63, 70, 78, 84, 91, 105, 126, 140, 168, 189, 238, 294, 336, 483, 630, 924, 1806

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

• nonn
• fini
• full
• easy

Comments

The number k=42 is explicitly included, treating the result of division through zero as an integer.

Row 42 of A191973.

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A191973.

Programs

Maple

for m from 1 to 1806 do if(m=42 or m*42 mod (m-42) = 0)then printf("%d, ", m): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

f[a_,b_]:=(a*b)/(a-b); a=42;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Join[{42},Select[Range[2000],IntegerQ[(42#)/(42-#)]&]]//Quiet//Sort (* Harvey P. Dale, Mar 14 2020 *)

Extensions

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