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

Author

Hans Havermann, Jul 28 2017

Keywords

• nonn
• base
• fini

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

Examples

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

Links

• Hans Havermann, Table of n, a(n) for n = 1..10000
• Hans Havermann, Pandigital factorization integer cascades

Crossrefs

Cf. A058909, A288818.

Programs

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 *)