cp's OEIS Frontend

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).

%I A374317 #14 Jul 07 2024 01:32:10
%S A374317 1,2,6,6,30,20,140,70,70,7,77,8316,108108,858,5720,1430,24310,48620,
%T A374317 923780,46189,3879876,176358,4056234,2704156,676039,104006,312018,
%U A374317 44574,1292646,4308820,133573420,267146840,2203961430,259289580,363005412,3267048708
%N 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).
%C A374317 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.
%C A374317 Unlike A008336, this sequence contains several repeated terms.
%H A374317 Rémy Sigrist, <a href="/A374317/b374317.txt">Table of n, a(n) for n = 1..1000</a>
%H A374317 Rémy Sigrist, <a href="/A374317/a374317.png">Colored representation of b_n(k) for n <= 1000</a> (where the color at (x, y) is function of b_x(y))
%e A374317 The first terms, alongside the corresponding sequences b_n, are:
%e A374317   n   a(n)  b_n
%e A374317   --  ----  ----------------------------------------------
%e A374317    1     1  [1, 1]
%e A374317    2     2  [2, 2, 1]
%e A374317    3     6  [6, 6, 3, 1]
%e A374317    4     6  [6, 6, 12, 4, 1]
%e A374317    5    30  [30, 30, 60, 20, 5, 1]
%e A374317    6    20  [20, 20, 40, 120, 30, 6, 1]
%e A374317    7   140  [140, 140, 280, 840, 210, 42, 7, 1]
%e A374317    8    70  [70, 70, 140, 420, 1680, 336, 56, 8, 1]
%e A374317    9    70  [70, 70, 35, 105, 420, 84, 504, 72, 9, 1]
%e A374317   10     7  [7, 7, 14, 42, 168, 840, 5040, 720, 90, 10, 1]
%o A374317 (PARI) a(n) = { my (b = 1); forstep (k = n, 1, -1, if (b % k==0, b /= k, b *= k);); return (b); }
%Y A374317 Cf. A008336, A374318.
%K A374317 nonn
%O A374317 1,2
%A A374317 _Rémy Sigrist_, Jul 04 2024