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A290385 Base-ten pandigital factorization integers. The normal factorization (primes raised to greater-than-one exponents) of these numbers uses each digit exactly once. 1
15618090, 20824120, 22022490, 22816290, 22908090, 23294190, 23427135, 23507490, 24843120, 26104560, 26152080, 26679990, 27114690, 27687090, 28275690, 29218704, 29363320, 29447898, 29544690, 29582490, 29670378, 29688144, 29910138, 30120144 (list; graph; refs; listen; history; text; internal format)
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: A186050 A121840 A004673 * A058909 A179585 A105650

Adjacent sequences:  A290382 A290383 A290384 * A290386 A290387 A290388

KEYWORD

nonn,base,fini

AUTHOR

Hans Havermann, Jul 28 2017

STATUS

approved

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Last modified August 22 01:16 EDT 2017. Contains 290942 sequences.