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

10968, 28651, 43610, 48960, 50841, 65821, 80416, 90584

Offset: 1

Author

Tanya Khovanova, Dec 23 2006

Keywords

• base
• fini
• full
• nonn

Comments

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

Examples

			10968 = 2^3 * 3 * 457.
		

Crossrefs

Cf. A273260: similar, but digits of exponents > 1 in the prime factorization are also taken into account.

Programs

Maple

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

Mathematica

Select[Range[2, 1000000], Sort[Join[IntegerDigits[ # ], Flatten[IntegerDigits[Transpose[FactorInteger[ # ]][[1]]]]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]

PARI

is_A124668(n) = { vecsum([logint(f,10)+1 | f<-n=concat(factor(n)[,1], n)])==10 && #Set(concat([digits(f) | f<-n]))>9 }
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