A307547 a(n) is the smallest divisor of the partition number P(n) = A000041(n) not already in the sequence.

1, 2, 3, 5, 7, 11, 15, 22, 6, 14, 4, 77, 101, 9, 8, 21, 27, 35, 10, 19, 12, 167, 251, 25, 89, 28, 43, 13, 55, 467, 311, 23, 49, 1231, 33, 17977, 281, 121, 45, 42, 193, 2417, 71, 31, 41, 73, 38, 7013, 275, 9283, 363, 53, 63, 17, 142, 47, 102359, 20, 44, 139

Offset: 1

Author

Rémy Sigrist, Jul 27 2019

Keywords

• nonn

Comments

Provided A046641(m) is defined for any number m > 0, this sequence is a permutation of the natural numbers.

Examples

			The first terms, alongside the divisors of P(n), are:
  n   a(n)  div(P(n))
  --  ----  --------------------
   1     1  (1)
   2     2  (1, 2)
   3     3  (1, 3)
   4     5  (1, 5)
   5     7  (1, 7)
   6    11  (1, 11)
   7    15  (1, 3, 5, 15)
   8    22  (1, 2, 11, 22)
   9     6  (1, 2, 3, 5, 6, 10, 15, 30)
  10    14  (1, 2, 3, 6, 7, 14, 21, 42)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5000
• Rémy Sigrist, PARI program for A307547

Crossrefs

Cf. A000041, A046641, A049575, A309200.

Programs

PARI

See Links section.

Formula

a(A049575(k)) = A049575(k).