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

Author

Rémy Sigrist, Jul 28 2019

Keywords

• nonn

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.

Examples

			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)
		

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

Crossrefs

Cf. A018252, A093641, A111273.

Programs

PARI

See Links section.