A374317 For any n > 0, let b_n(n+1) = 1, and for k = 1..n, if k divides b_n(k+1) then b_n(k) = b_n(k+1) / k otherwise b_n(k) = b_n(k+1) * k; a(n) = b_n(1).

1, 2, 6, 6, 30, 20, 140, 70, 70, 7, 77, 8316, 108108, 858, 5720, 1430, 24310, 48620, 923780, 46189, 3879876, 176358, 4056234, 2704156, 676039, 104006, 312018, 44574, 1292646, 4308820, 133573420, 267146840, 2203961430, 259289580, 363005412, 3267048708

Offset: 1

Author

Rémy Sigrist, Jul 04 2024

Keywords

• nonn

Comments

This sequence is a variant of A008336; here we divide or multiply by numbers from n down to 1, there by numbers from 1 up to n.

Unlike A008336, this sequence contains several repeated terms.

Examples

			The first terms, alongside the corresponding sequences b_n, are:
  n   a(n)  b_n
  --  ----  ----------------------------------------------
   1     1  [1, 1]
   2     2  [2, 2, 1]
   3     6  [6, 6, 3, 1]
   4     6  [6, 6, 12, 4, 1]
   5    30  [30, 30, 60, 20, 5, 1]
   6    20  [20, 20, 40, 120, 30, 6, 1]
   7   140  [140, 140, 280, 840, 210, 42, 7, 1]
   8    70  [70, 70, 140, 420, 1680, 336, 56, 8, 1]
   9    70  [70, 70, 35, 105, 420, 84, 504, 72, 9, 1]
  10     7  [7, 7, 14, 42, 168, 840, 5040, 720, 90, 10, 1]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..1000
• Rémy Sigrist, Colored representation of b_n(k) for n <= 1000 (where the color at (x, y) is function of b_x(y))

Crossrefs

Cf. A008336, A374318.

Programs

PARI

a(n) = { my (b = 1); forstep (k = n, 1, -1, if (b % k==0, b /= k, b *= k);); return (b); }