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%I #7 Aug 12 2015 02:18:02
%S 10968,28651,43610,48960,50841,65821,80416,90584
%N Numbers that together with their prime factors contain every digit exactly once.
%e 10968 = 2^3 * 3 * 457.
%p isA124668 := proc(n) local digs,digs2,f,fac,b ; digs := convert(n,base,10) ; f := ifactors(n)[2] ; for fac from 1 to nops(f) do b := op(1,op(fac,f)) ; digs := [op(digs),op(convert(b,base,10))] ; od ; digs2 := convert(digs,set) ; if nops(digs2) = 10 and nops(digs2)=nops(digs) then print(n,f) ; RETURN(true) ; else RETURN(false) ; fi ; end : A124668aux := proc(n,dleft) local i,nnxt,dnxt ; isA124668(n) : for i from 1 to nops(dleft) do nnxt := 10*n+op(i,dleft) ; dnxt := dleft minus {op(i,dleft)} ; if nops(dnxt) > 0 then A124668aux(nnxt,dnxt) ; fi ; od ; end : dleft := {0,1,2,3,4,5,6,7,8,9} : for i from 1 to 9 do dnxt := dleft minus {i} ; A124668aux(i,dnxt) : od : # _R. J. Mathar_, Jan 13 2007
%t Select[Range[2, 1000000], Sort[Join[IntegerDigits[ # ], Flatten[IntegerDigits[Transpose[FactorInteger[ # ]][[1]]]]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]
%K base,fini,full,nonn
%O 1,1
%A _Tanya Khovanova_, Dec 23 2006
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