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A263130 Least number such that the product of its digits in factorial base is n. 2
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: 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

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Last modified January 30 07:19 EST 2023. Contains 359939 sequences. (Running on oeis4.)