A113623 7-smooth numbers containing only noncomposite digits (1,2,3,5,7).

1, 2, 3, 5, 7, 12, 15, 21, 25, 27, 32, 35, 72, 75, 112, 125, 135, 175, 225, 252, 315, 375, 512, 525, 735, 1125, 1152, 1215, 1225, 1323, 1372, 1512, 1575, 1715, 2352, 3125, 3375, 13122, 13125, 15552, 25515, 25725, 31752, 35721, 55125, 77175, 111132

Offset: 1

Author

Amarnath Murthy, Nov 10 2005

Keywords

• base
• nonn

Examples

			175 is a term since 175 = 5^2*7 and contains digits 1,5,7 none of which is composite. 175 is a member of A002473.
		

Crossrefs

Intersection of A001742 and A002473.

Cf. A113624.

Programs

Maple

isA002473 := proc(n) local ifs ; if n <= 10 then true ; else ifs := ifactors(n)[2] ; if max( seq(op(1,i),i=ifs) ) <= 7 then true; else false ; fi ; fi ; end: isA113623 := proc(n) local digs ; if isA002473(n) then if convert(convert(n,base,10),set) minus {1,2,3,5,7} <> {} then false ; else true ; fi ; else false ; fi ; end: for n from 1 to 150000 do if isA113623(n) then printf("%d, ",n) ; fi ; od; # R. J. Mathar, Aug 28 2007

Extensions

More terms from R. J. Mathar, Aug 28 2007

Name corrected by Andrew Howroyd, Sep 17 2024