A326776 a(n) is the smallest divisor of the n-th nonprime number (A018252(n)) not already in the sequence.

1, 2, 3, 4, 9, 5, 6, 7, 15, 8, 18, 10, 21, 11, 12, 25, 13, 27, 14, 30, 16, 33, 17, 35, 36, 19, 39, 20, 42, 22, 45, 23, 24, 49, 50, 51, 26, 54, 55, 28, 57, 29, 60, 31, 63, 32, 65, 66, 34, 69, 70, 72, 37, 75, 38, 77, 78, 40, 81, 41, 84, 85, 43, 87, 44, 90, 91

Offset

1,2

Comments

This sequence is a permutation of the natural numbers.

Empirically:

- the subsequence with the terms satisfying a(n) <= n correspond to A093641,

- if a(n) > n, then a(n) = A018252(n),

- these two situations appear as two lines in the scatterplot of the sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A326776

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the divisors of A018252(n), are:
  n   a(n)  div(A018252(n))
  --  ----  ---------------
   1     1  (1)
   2     2  (1, 2, 4)
   3     3  (1, 2, 3, 6)
   4     4  (1, 2, 4, 8)
   5     9  (1, 3, 9)
   6     5  (1, 2, 5, 10)
   7     6  (1, 2, 3, 4, 6, 12)
   8     7  (1, 2, 7, 14)
   9    15  (1, 3, 5, 15)
  10     8  (1, 2, 4, 8, 16)

Prog

(PARI) See Links section.

Crossrefs

Cf. A018252, A093641, A111273.

Sequence in context: A124418 A175177 A303951 * A249746 A112480 A298196

Adjacent sequences: A326773 A326774 A326775 * A326777 A326778 A326779

Keyword

nonn

Author

Rémy Sigrist, Jul 28 2019

Status

approved