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

1,2

Comments

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

Links

Table of n, a(n) for n=1..87.

Rémy Sigrist, PARI program for A345874

Index entries for sequences related to binary expansion of n

Index entries for sequences related to divisors

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.

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000005, A065157.

Sequence in context: A087458 A052180 A065151 * A338720 A320013 A299990

Adjacent sequences: A345871 A345872 A345873 * A345875 A345876 A345877

Keyword

nonn,base

Author

Rémy Sigrist, Jun 27 2021

Status

approved