A290385 Base-ten pandigital factorization integers. The normal factorization (primes raised to greater-than-one exponents) of these numbers uses each digit exactly once.

15618090, 20824120, 22022490, 22816290, 22908090, 23294190, 23427135, 23507490, 24843120, 26104560, 26152080, 26679990, 27114690, 27687090, 28275690, 29218704, 29363320, 29447898, 29544690, 29582490, 29670378, 29688144, 29910138, 30120144

Offset

1,1

Comments

The sequence contains 14856143 terms, the largest being 7^986543210.

The corresponding zeroless sequence contains 2295201 terms, from 2992890 = 2*3*5*67*1489 to 7^98654321. - Giovanni Resta, Jul 29 2017

Links

Hans Havermann, Table of n, a(n) for n = 1..10000

Hans Havermann, Pandigital factorization integer cascades

Example

20824120 is in the sequence because 2^3*5*487*1069 is pandigital.

Mathematica

pop[d_, mn_] := Union @@ Table[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[d, {k}], 1], # > mn && PrimeQ[#] &], {k, IntegerLength@ mn, Length[d]}]; ric[w_, d_, p_] := If[d == {}, cnt++; If[Max[Last /@ w] < 30 && Times @@ (Power @@@ w) <= 4*10^7, AppendTo[L, w]], Block[{pp = pop[d, p], v}, Do[v = Complement[d, IntegerDigits@ x]; ric[Append[w, {x, 1}], v, x]; Do[If[e > 1, ric[Append[w, {x, e}], Complement[v, IntegerDigits@e], x]], {e, Union[ FromDigits /@ Flatten[ Permutations /@ Subsets[v, {1, Length@v}], 1]]}], {x, pp}]]]; Monitor[cnt = 0; L = {}; ric[{}, Range[0, 9], 1]; , cnt]; Print["cnt = ", cnt]; Sort[(Times @@ (Power @@@ #)) & /@ L] (* Giovanni Resta, Jul 29 2017 *)

Crossrefs

Cf. A058909, A288818.

Sequence in context: A345618 A346335 A004673 * A058909 A179585 A105650

Adjacent sequences: A290382 A290383 A290384 * A290386 A290387 A290388

Keyword

nonn,base,fini

Author

Hans Havermann, Jul 28 2017

Status

approved