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
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.
Programs
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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