A337908 a(n) is the number of nonempty intervals x..y (with 0 < x <= y) such that LCM(x..y) = n.

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, 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, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

This sequence is unbounded.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

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

Example

The first terms, alongside the corresponding intervals, are:
  n   a(n)  {x..y}
  --  ----  --------------------------
   1     1  {1..1}
   2     2  {1..2, 2..2}
   3     1  {3..3}
   4     1  {4..4}
   5     1  {5..5}
   6     3  {1..3, 2..3, 6..6}
   7     1  {7..7}
   8     1  {8..8}
   9     1  {9..9}
  10     1  {10..10}
  11     1  {11..11}
  12     4  {1..4, 2..4, 3..4, 12..12}
  13     1  {13..13}
  14     1  {14..14}
  15     1  {15..15}

Prog

(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 }

Crossrefs

Cf. A003418.

Sequence in context: A355662 A069897 A257242 * A325789 A356352 A175597

Adjacent sequences: A337905 A337906 A337907 * A337909 A337910 A337911

Keyword

nonn

Author

Rémy Sigrist, Sep 29 2020

Status

approved