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User: Albert ten Oever

Albert ten Oever has authored 1 sequences.

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

Albert ten Oever, Mar 20 2019

nonn

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.

			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.

Albert ten Oever, Python program

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

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

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User: Albert ten Oever

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

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