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A124668 Numbers that together with their prime factors contain every digit exactly once.

%I A124668 #13 Jun 05 2024 04:25:46
%S A124668 10968,28651,43610,48960,50841,65821,80416,90584
%N A124668 Numbers that together with their prime factors contain every digit exactly once.
%C A124668 The exponents in the prime factorization are not considered here. See A273260 for that variant, which contains, e.g., 26487 = 3^5 * 109 and 61054 = 2 * 7^3 * 89. - _M. F. Hasler_, May 28 2024
%e A124668 10968 = 2^3 * 3 * 457.
%p A124668 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 A124668 Select[Range[2, 1000000], Sort[Join[IntegerDigits[ # ], Flatten[IntegerDigits[Transpose[FactorInteger[ # ]][[1]]]]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]
%o A124668 (PARI) is_A124668(n) = { vecsum([logint(f,10)+1 | f<-n=concat(factor(n)[,1], n)])==10 && #Set(concat([digits(f) | f<-n]))>9 }
%o A124668 L=List(); forvec(v=vector(5, i, [0, 9]), forperm(v, n, is_A124668(n=fromdigits(Vec(n)))&& listput(L, n)),2); A124668=Set(L) \\ _M. F. Hasler_, Jun 05 2024
%Y A124668 Cf. A273260: similar, but digits of exponents > 1 in the prime factorization are also taken into account.
%K A124668 base,fini,full,nonn
%O A124668 1,1
%A A124668 _Tanya Khovanova_, Dec 23 2006