A307032 - OEIS

%I #24 Dec 11 2019 08:54:09

%S 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,

%T 30,26,32,23,33,36,35,40,34,42,29,39,45,38,48,44,31,49,50,54,46,52,51,

%U 56,55,60,37,63,64,57,41,43,66,65,70,72,58,68,75,47,62

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

%C 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.

%H Albert ten Oever, <a href="https://bitbucket.org/agtoever/a307032">Python program</a>

%e Generation of the first five elements:

%e - Start with the natural numbers: 1, 2, 3, 4, 5.

%e - Prime factorization of those numbers: 1, 2, 3, 2*2, 5.

%e - Sum of prime factors: 0, 2, 3, 4, 5.

%e - Now move each element:

%e     - Move 1 0 steps: 1, 2, 3, 4, 5.

%e     - Move 2 2 steps: 1, 3, 4, 2, 5.

%e     - Move 3 3 steps: 1, 4, 2, 5, 3.

%e     - Move 4 4 steps: 1, 2, 5, 3, 6, 4 (needed to extend range to move 4)

%e     - Move 5 5 steps: 1, 2, 3, 6, 4, 7, 8, 5 (needed to extend range to move 5)

%e     - Because 6, 7, 8 and 9 are also moved to the right, the first 5 elements are: 1, 2, 3, 4, 5.

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

%K nonn

%O 1,2

%A _Albert ten Oever_, Mar 20 2019

%E Corrected sequence caused by an error in the Python code generating the sequence. Edited by _Albert ten Oever_, Mar 24 2019