A263130 Least number such that the product of its digits in factorial base is n.

1, 5, 21, 17, 633, 23, 36153, 65, 93, 635, 443122713, 71, 81474226713, 36155, 645, 113, 6069010670156313, 95, 2318037293294156313, 641, 36165, 443122715, 595774037991797891660313, 119, 4233, 81474226715, 453, 36161, 256727294482662730300616548940313, 647

Offset: 1

Author

Paul Tek, Oct 10 2015

Keywords

• nonn
• base

Comments

The product of digits in factorial base is given by A208575.

All terms are odd.

Each prime number sets a new record.

a(p) = p*(p!) + Sum_{k=1..p-1} k! for any prime p.

a(n!) = A033312(n+1) for any n>0.

A208576(a(n)) = A208576(n)+1 for any n>1.

Examples

			The first terms of the sequence are:
+----+-------------+----------------------------+
| n  | a(n)        | a(n) in factorial base     |
+----+-------------+----------------------------+
|  1 |           1 |                          1 |
|  2 |           5 |                        2_1 |
|  3 |          21 |                      3_1_1 |
|  4 |          17 |                      2_2_1 |
|  5 |         633 |                  5_1_1_1_1 |
|  6 |          23 |                      3_2_1 |
|  7 |       36153 |              7_1_1_1_1_1_1 |
|  8 |          65 |                    2_2_2_1 |
|  9 |          93 |                    3_3_1_1 |
| 10 |         635 |                  5_1_1_2_1 |
| 11 |   443122713 |     11_1_1_1_1_1_1_1_1_1_1 |
| 12 |          71 |                    2_3_2_1 |
| 13 | 81474226713 | 13_1_1_1_1_1_1_1_1_1_1_1_1 |
| 14 |       36155 |              7_1_1_1_1_2_1 |
| 15 |         645 |                  5_1_3_1_1 |
| 16 |         113 |                    4_2_2_1 |
+----+-------------+----------------------------+
		

Links

• Paul Tek, Table of n, a(n) for n = 1..448
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A033312, A200748, A208277, A208575, A208576.

Programs

Mathematica

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 *)