A345874 a(n) is the number of distinct pairs of positive integers (u, v) such that A065157(u, v) = n.

1, 2, 2, 3, 2, 3, 2, 4, 2, 4, 2, 4, 2, 3, 3, 5, 2, 4, 2, 5, 2, 3, 2, 5, 2, 3, 3, 4, 2, 4, 2, 6, 2, 4, 2, 6, 2, 3, 2, 6, 2, 4, 2, 4, 3, 3, 2, 6, 2, 3, 3, 4, 2, 5, 2, 5, 2, 3, 2, 5, 2, 3, 4, 7, 2, 4, 2, 6, 2, 3, 2, 7, 2, 4, 2, 4, 2, 3, 2, 7, 2, 4, 2, 5, 3, 3, 2

Offset: 1

Author

Rémy Sigrist, Jun 27 2021

Keywords

• nonn
• base

Comments

If A065157(u, v) = n then u is a divisor of n.

Examples

			For n = 10:
- the table A065157(u, v) begins (with terms > 10 replaced by dots):
  u\v|   1   2   3  4  5  6  7  8  9  10
  ---+----------------------------------
    1|   1   2   3  4  5  6  7  8  9  10
    2|   2   4  10  8  .  .  .  .  .  .
    3|   3   6  .   .  .  .  .  .  .  .
    4|   4   8  .   .  .  .  .  .  .  .
    5|   5  10  .   .  .  .  .  .  .  .
    6|   6  .   .   .  .  .  .  .  .  .
    7|   7  .   .   .  .  .  .  .  .  .
    8|   8  .   .   .  .  .  .  .  .  .
    9|   9  .   .   .  .  .  .  .  .  .
   10|  10  .   .   .  .  .  .  .  .  .
- the value 10 appears 4 times,
- so a(10) = 4.
		

Links

• Rémy Sigrist, PARI program for A345874
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to divisors

Crossrefs

Cf. A000005, A065157.

Programs

PARI

See Links section.

Formula

a(n) <= A000005(n).

a(n) >= 2 for any n > 1 (as A065157(1, n) = A065157(n, 1) = n).

a(2^k) = k + 1 for any k >= 0.

a(2^k - 1) = A000005(k) for any k > 0.