A162693 Strictly positive numbers n such that 30*n/(30+n) are integers.

6, 15, 20, 30, 45, 60, 70, 120, 150, 195, 270, 420, 870

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 10 2009

Keywords

• nonn
• fini
• full

Comments

The 30th row of A127730.

The ansatz 30*n/(30+n)=j (any integer j) yields n=30*j/(30-j) which demonstrates that the sequence is finite if n>=0. [R. J. Mathar, Jul 13 2009]

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692

Cf. A127730. [From Franklin T. Adams-Watters, Aug 07 2009]

Programs

Mathematica

f[a_,b_]:=(a*b)/(a+b); a=30;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]],AppendTo[lst,n]],{n,9!}];lst
Select[Range[1000],IntegerQ[(30#)/(30+#)]&] (* Harvey P. Dale, Sep 25 2019 *)

Extensions

Edited by R. J. Mathar, Jul 13 2009