A337908 - OEIS

%I #9 Dec 12 2021 22:53:33

%S 1,2,1,1,1,3,1,1,1,1,1,4,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,

%T 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,8,1,1,1,1,1,1,1,1,

%U 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N a(n) is the number of nonempty intervals x..y (with 0 < x <= y) such that LCM(x..y) = n.

%C This sequence is unbounded.

%H Antti Karttunen, <a href="/A337908/b337908.txt">Table of n, a(n) for n = 1..65537</a>

%F a(p) = 1 for any odd prime number p.

%e The first terms, alongside the corresponding intervals, are:

%e   n   a(n)  {x..y}

%e   --  ----  --------------------------

%e    1     1  {1..1}

%e    2     2  {1..2, 2..2}

%e    3     1  {3..3}

%e    4     1  {4..4}

%e    5     1  {5..5}

%e    6     3  {1..3, 2..3, 6..6}

%e    7     1  {7..7}

%e    8     1  {8..8}

%e    9     1  {9..9}

%e   10     1  {10..10}

%e   11     1  {11..11}

%e   12     4  {1..4, 2..4, 3..4, 12..12}

%e   13     1  {13..13}

%e   14     1  {14..14}

%e   15     1  {15..15}

%o (PARI) a(n) = { my (v=0); fordiv (n, x, my (l=1); for (y=x, oo, l=lcm(l,y); if (l>n, break, l==n, v++))); v }

%Y Cf. A003418.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Sep 29 2020