The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A351362 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A351362

Number of ways the numbers from 1..n do not divide the numbers from n..2n-1.
(history; published version)

#18 by Alois P. Heinz at Mon Oct 23 17:21:20 EDT 2023

STATUS

proposed

approved

#17 by Chai Wah Wu at Mon Oct 23 17:19:23 EDT 2023

STATUS

editing

proposed

#16 by Chai Wah Wu at Mon Oct 23 17:19:18 EDT 2023

PROG

(Python)

from math import isqrt

def A351362(n): return ((t:=isqrt(m:=(n<<1)-1))+(s:=isqrt(r:=n-1)))*(t-s)+(sum(r//k for k in range(1, s+1))-sum(m//k for k in range(1, t+1))<<1)+n*(n+1)-1 # Chai Wah Wu, Oct 23 2023

STATUS

approved

editing

#15 by Wesley Ivan Hurt at Thu Feb 10 22:04:53 EST 2022

STATUS

editing

approved

#14 by Wesley Ivan Hurt at Thu Feb 10 22:04:49 EST 2022

EXAMPLE

a(5) = 14; there are 14 ways that the numbers 1..5 do not divide the numbers 5..9. 2 does not divide 5,7,9 (3 ways) + 3 does not divide 5,7,8 (3 ways) + 4 does not divide 5,6,7,9 (4 ways) + 5 does not divide 6,7,8,9 (4 ways) = 14 ways.

STATUS

approved

editing

#13 by Michael De Vlieger at Wed Feb 09 09:05:11 EST 2022

STATUS

reviewed

approved

#12 by Joerg Arndt at Wed Feb 09 08:59:16 EST 2022

STATUS

proposed

reviewed

#11 by Wesley Ivan Hurt at Wed Feb 09 08:35:55 EST 2022

STATUS

editing

proposed

#10 by Wesley Ivan Hurt at Wed Feb 09 08:35:30 EST 2022

NAME

Number of ways the numbers from 1..n do not divide the numbers from n..2n-1, for n >= 2.

DATA

0, 1, 4, 8, 14, 22, 32, 42, 57, 72, 88, 108, 129, 151, 177, 203, 232, 262, 295, 329, 367, 405, 443, 487, 532, 577, 627, 675, 727, 783, 839, 895, 956, 1018, 1082, 1148, 1217, 1285, 1357, 1431, 1506, 1586, 1664, 1746, 1832, 1914, 2002, 2092, 2186, 2277, 2374, 2472, 2568, 2672

OFFSET

2,2

1,3

STATUS

proposed

editing

#9 by Michel Marcus at Tue Feb 08 23:56:23 EST 2022

STATUS

editing

proposed