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

1,2

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.

Links

Paul Tek, Table of n, a(n) for n = 1..448

Paul Tek, PERL program for this sequence

Example

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 |
+----+-------------+----------------------------+

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 *)

Crossrefs

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

Sequence in context: A167202 A204914 A355036 * A165204 A043053 A004163

Adjacent sequences: A263127 A263128 A263129 * A263131 A263132 A263133

Keyword

nonn,base

Author

Paul Tek, Oct 10 2015

Status

approved