A273260 -id:A273260 - cp's OEIS frontend

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

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

Offset: 1

Tanya Khovanova, Dec 23 2006

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

			10968 = 2^3 * 3 * 457.

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

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

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

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

A281335 a(n) is the smallest composite number having the same base-n digits (both type and quantity) as the primes and greater-than-one exponents in its factorization.

Original entry on oeis.org

25, 16, 25, 2312, 16, 7136, 27, 72646, 25, 4617, 169, 384, 4119, 3875, 289, 182585, 128, 556875, 451, 49, 529, 1012985, 679, 72420352, 42752, 585903, 841, 64, 961, 118375, 1285, 2944, 179503, 4624625, 1369

Offset: 2

Hans Havermann, Jan 20 2017

			In base 2: The digits of 25 (11001) are the same type and quantity as the total of the prime 5 (101) and its exponent 2 (10) in 25's factorization; 2 zeros, 3 ones.
In base 26: The digits of 42752 (2,11,6,8) are the same type and quantity as the total of the prime 2 (2) and its exponent 8 (8) and the prime 167 (6,11) in 42752's factorization; 1 each of two, six, eight, eleven.

Cf. A273260, A281336.

cp's OEIS Frontend

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

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