A343505 a(n) is the least common multiple of the nonzero digits in factorial base expansion of 1/n.

1, 1, 2, 2, 4, 1, 6, 3, 6, 2, 60, 2, 120, 3, 3, 6, 1008, 4, 51480, 1, 4, 30, 6930, 1, 140, 36, 60, 20, 16380, 4, 243374040, 12, 105, 504, 12, 6, 6126120, 4680, 168, 3, 314954640, 10, 209969760, 24, 4, 180180, 1790848659600, 6, 924, 6, 660, 1260, 8303710615200

Offset: 1

Author

Rémy Sigrist, Apr 17 2021

Keywords

• nonn
• look
• base

Comments

See the Wikipedia link for the construction method of 1/n in factorial base.

Examples

			The first terms, alongside 1/n in factorial base, are:
  n   a(n)   1/n in factorial base
  --  -----  -----------------------------------------
   1      1  1
   2      1  0.1
   3      2  0.0 2
   4      2  0.0 1 2
   5      4  0.0 1 0 4
   6      1  0.0 1
   7      6  0.0 0 3 2 0 6
   8      3  0.0 0 3
   9      6  0.0 0 2 3 2
  10      2  0.0 0 2 2
  11     60  0.0 0 2 0 5 3 1 4 0 10
  12      2  0.0 0 2
  13    120  0.0 0 1 4 1 2 5 4 8 5 0 12
  14      3  0.0 0 1 3 3 3
  15      3  0.0 0 1 3
  16      6  0.0 0 1 2 3
  17   1008  0.0 0 1 2 0 2 3 6 8 9 0 9 2 7 0 16
  18      4  0.0 0 1 1 4
  19  51480  0.0 0 1 1 1 6 2 0 9 5 2 6 11 11 13 8 0 18
  20      1  0.0 0 1 1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5000
• Rémy Sigrist, Colored logarithmic scatterplot of the sequence for n = 1..25000 (where the color is function of A052126(n))
• Wikipedia, Factorial number system (Fractional values)
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A052126, A294168, A343504.

Programs

PARI

a(n) = my (v=1, f=1/n); for (r=2, oo, if (f==0, return (v), floor(f), v=lcm(v, floor(f))); f=frac(f)*r)