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A263130 Least number such that the product of its digits in factorial base is n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A053003 A167202 A204914 * A165204 A043053 A004163

Adjacent sequences:  A263127 A263128 A263129 * A263131 A263132 A263133

KEYWORD

nonn,base

AUTHOR

Paul Tek, Oct 10 2015

STATUS

approved

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Last modified January 27 05:34 EST 2021. Contains 340454 sequences. (Running on oeis4.)