A382377 -id:A382377 - cp's OEIS frontend

A382375 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of n and a(n) differ exactly by one.

2, 1, 4, 3, 6, 5, 9, 10, 7, 8, 14, 15, 21, 11, 12, 18, 22, 16, 25, 24, 13, 17, 26, 20, 19, 23, 33, 34, 35, 36, 38, 40, 27, 28, 29, 30, 39, 31, 37, 32, 46, 49, 51, 54, 55, 41, 57, 56, 42, 58, 43, 60, 62, 44, 45, 48, 47, 50, 65, 52, 69, 53, 74, 72, 59, 77, 82

Offset: 1

Rémy Sigrist, Mar 23 2025

nonn

A self-inverse permutation of the positive integers.

			The initial terms are:
  n   a(n)  A001222(n)  A001222(a(n))
  --  ----  ----------  -------------
   1     2           0              1
   2     1           1              0
   3     4           1              2
   4     3           2              1
   5     6           1              2
   6     5           2              1
   7     9           1              2
   8    10           3              2
   9     7           2              1
  10     8           2              3
  11    14           1              2
  12    15           3              2
  13    21           1              2
  14    11           2              1
  15    12           2              3

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A001222, A382374, A382377.

PARI
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A382376 Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of adjacent terms differ exactly by one.

Original entry on oeis.org

1, 2, 6, 3, 10, 4, 12, 5, 14, 7, 15, 8, 18, 9, 20, 11, 21, 13, 22, 16, 24, 17, 26, 19, 28, 23, 33, 25, 34, 27, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 44, 41, 45, 42, 46, 43, 48, 47, 50, 49, 51, 53, 52, 59, 54, 60, 55, 61, 56, 64, 57, 66, 58, 67, 62, 70, 63

Offset: 1

Rémy Sigrist, Mar 23 2025

nonn

All primorial numbers appear in the sequence (we can use similar arguments as for A382357).

Conjecture: this sequence is a permutation of the positive integers.

			The initial terms are:
  n   a(n)  A001221(a(n))
  --  ----  -------------
   1     1              0
   2     2              1
   3     6              2
   4     3              1
   5    10              2
   6     4              1
   7    12              2
   8     5              1
   9    14              2
  10     7              1
  11    15              2
  12     8              1
  13    18              2
  14     9              1
  15    20              2

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

Cf. A001221, A382357, A382374, A382377.

PARI
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cp's OEIS Frontend

A382375 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of n and a(n) differ exactly by one.

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