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

1,2

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..5000

Rémy Sigrist, PARI program for A307547

Formula

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

Example

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)

Prog

(PARI) See Links section.

Crossrefs

Cf. A000041, A046641, A049575, A309200.

Sequence in context: A027342 A363231 A184643 * A182804 A242695 A319473

Adjacent sequences: A307544 A307545 A307546 * A307548 A307549 A307550

Keyword

nonn

Author

Rémy Sigrist, Jul 27 2019

Status

approved