A307032 Permutation of the positive integers formed by moving each number the sum of its prime factors to the right.

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 11, 14, 15, 16, 18, 13, 20, 21, 17, 24, 22, 25, 27, 19, 28, 30, 26, 32, 23, 33, 36, 35, 40, 34, 42, 29, 39, 45, 38, 48, 44, 31, 49, 50, 54, 46, 52, 51, 56, 55, 60, 37, 63, 64, 57, 41, 43, 66, 65, 70, 72, 58, 68, 75, 47, 62

Offset

1,2

Comments

To generate this sequence, start with a list of the positive integers. For each positive integer, calculate the sum of its prime factors (with multiplicity) and move each element that numbers of positions to the right in the sequence. This is a permutation of the positive integers. All prime numbers appear in increasing order.

Links

Table of n, a(n) for n=1..67.

Albert ten Oever, Python program

Example

Generation of the first five elements:
- Start with the natural numbers: 1, 2, 3, 4, 5.
- Prime factorization of those numbers: 1, 2, 3, 2*2, 5.
- Sum of prime factors: 0, 2, 3, 4, 5.
- Now move each element:
    - Move 1 0 steps: 1, 2, 3, 4, 5.
    - Move 2 2 steps: 1, 3, 4, 2, 5.
    - Move 3 3 steps: 1, 4, 2, 5, 3.
    - Move 4 4 steps: 1, 2, 5, 3, 6, 4 (needed to extend range to move 4)
    - Move 5 5 steps: 1, 2, 3, 6, 4, 7, 8, 5 (needed to extend range to move 5)
    - Because 6, 7, 8 and 9 are also moved to the right, the first 5 elements are: 1, 2, 3, 4, 5.

Crossrefs

Cf. A001414 (sum of primes dividing n, with repetition).

Sequence in context: A073289 A122349 A127388 * A273859 A332073 A117332

Adjacent sequences: A307029 A307030 A307031 * A307033 A307034 A307035

Keyword

nonn

Author

Albert ten Oever, Mar 20 2019

Extensions

Corrected sequence caused by an error in the Python code generating the sequence. Edited by Albert ten Oever, Mar 24 2019

Status

approved