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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

%I

%S 15618090,20824120,22022490,22816290,22908090,23294190,23427135,

%T 23507490,24843120,26104560,26152080,26679990,27114690,27687090,

%U 28275690,29218704,29363320,29447898,29544690,29582490,29670378,29688144,29910138,30120144

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

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

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

%H Hans Havermann, <a href="/A290385/b290385.txt">Table of n, a(n) for n = 1..10000</a>

%H Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2017/07/pandigital-factorization-integer.html">Pandigital factorization integer cascades</a>

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

%t 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 *)

%Y Cf. A058909, A288818.

%K nonn,base,fini

%O 1,1

%A _Hans Havermann_, Jul 28 2017

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Last modified August 19 08:57 EDT 2017. Contains 290794 sequences.