A162825 Positive numbers k such that 60*k/(60-k) are integers.

10, 12, 15, 20, 24, 30, 35, 36, 40, 42, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 78, 80, 84, 85, 90, 96, 100, 105, 108, 110, 120, 132, 135, 140, 150, 160, 180, 204, 210, 240, 260, 285, 300, 360, 420

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 13 2009

Keywords

• nonn
• easy
• fini
• full

Comments

The number k=60 is explicitly included. The last entry in the sequence is a(68) = 3660.

Row 60 of A191973.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..68 (full sequence)

Crossrefs

Cf. A162688, A162689, A162690, A162691, A162692, A162693, A162694, A162817, A162818, A162819, A162820, A162821, A162822, A162823, A162824, A191973.

Programs

Maple

for n from 1 to 3660 do if(n=60 or type(60*n/(60-n),integer))then printf("%d, ",n): fi: od: # Nathaniel Johnston, Jun 22 2011

Mathematica

f[a_,b_]:=(a*b)/(a-b); a=60;lst={};Do[If[f[a,n]==IntegerPart[f[a,n]], AppendTo[lst,n]],{n,9!}];lst
Select[Range[500],If[#==60,True,IntegerQ[(60#)/(60-#)]]&] (* Harvey P. Dale, Sep 26 2023 *)

Extensions

Keyword fini added by R. J. Mathar, Jul 31 2009