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%I #14 Oct 27 2015 21:23:18
%S 1,5,21,17,633,23,36153,65,93,635,443122713,71,81474226713,36155,645,
%T 113,6069010670156313,95,2318037293294156313,641,36165,443122715,
%U 595774037991797891660313,119,4233,81474226715,453,36161,256727294482662730300616548940313,647
%N Least number such that the product of its digits in factorial base is n.
%C The product of digits in factorial base is given by A208575.
%C All terms are odd.
%C Each prime number sets a new record.
%C a(p) = p*(p!) + Sum_{k=1..p-1} k! for any prime p.
%C a(n!) = A033312(n+1) for any n>0.
%C A208576(a(n)) = A208576(n)+1 for any n>1.
%H Paul Tek, <a href="/A263130/b263130.txt">Table of n, a(n) for n = 1..448</a>
%H Paul Tek, <a href="/A263130/a263130.pl.txt">PERL program for this sequence</a>
%e The first terms of the sequence are:
%e +----+-------------+----------------------------+
%e | n | a(n) | a(n) in factorial base |
%e +----+-------------+----------------------------+
%e | 1 | 1 | 1 |
%e | 2 | 5 | 2_1 |
%e | 3 | 21 | 3_1_1 |
%e | 4 | 17 | 2_2_1 |
%e | 5 | 633 | 5_1_1_1_1 |
%e | 6 | 23 | 3_2_1 |
%e | 7 | 36153 | 7_1_1_1_1_1_1 |
%e | 8 | 65 | 2_2_2_1 |
%e | 9 | 93 | 3_3_1_1 |
%e | 10 | 635 | 5_1_1_2_1 |
%e | 11 | 443122713 | 11_1_1_1_1_1_1_1_1_1_1 |
%e | 12 | 71 | 2_3_2_1 |
%e | 13 | 81474226713 | 13_1_1_1_1_1_1_1_1_1_1_1_1 |
%e | 14 | 36155 | 7_1_1_1_1_2_1 |
%e | 15 | 645 | 5_1_3_1_1 |
%e | 16 | 113 | 4_2_2_1 |
%e +----+-------------+----------------------------+
%t f[n_] := Block[{d = Divisors@ n, g, k, m = {1}}, g[x_] := Flatten[Table[#1, {#2}] & @@@ FactorInteger@ x]; Do[k = Max@ Select[d, # <= i &]; If[! IntegerQ@ k, AppendTo[m, 1], d = Divisors[Last[d]/k]; AppendTo[m, k]]; If[d == {1}, Break[]], {i, 2, n}]; Reverse@ m]; Table[FromDigits[#, MixedRadix[Reverse@ Range[2, Length@ #]]] &@ f@ n, {n, 30}] (* _Michael De Vlieger_, Oct 12 2015, Version 10.2 *)
%Y Cf. A033312, A200748, A208277, A208575, A208576.
%K nonn,base
%O 1,2
%A _Paul Tek_, Oct 10 2015
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