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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).
2
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
1,2
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.
LINKS
Rémy Sigrist, Colored representation of b_n(k) for n <= 1000 (where the color at (x, y) is function of b_x(y))
EXAMPLE
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]
PROG
(PARI) a(n) = { my (b = 1); forstep (k = n, 1, -1, if (b % k==0, b /= k, b *= k); ); return (b); }
CROSSREFS
Sequence in context: A379582 A070889 A072744 * A056042 A056040 A333073
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 04 2024
STATUS
approved