Sums of distinct prime factors
(Dall.e creation ) We add two integers, we list the distinct prime factors of the result, we make the sum S of those factors. Example As we are in December 2023, let's consider the pair {12;2023}. 12 + 2023 = 2035 The distinct prime factors of 2035 are 5, 11 and 37. Their sum is S = 5 + 11 + 37 = 53. We will now propose a series of sequences related to the nature of this sum S (many thanks to Giorgos Kalogeropoulos for the computed terms and graphs!-) A ] Lexicographically earliest sequence of distinct positive integers such that the sum of the distinct prime factors of a(n) + a(n + 1) is a prime . A = 1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 12, 11, 13, 14, 15, 16, 18, 19, 17, 20, 21, 22, 25, 23, 24, 26, 27, 31, 28, 30, 29, 32, 35, 33, 34, 37, 36, 43, 38, 41, 39, 40, 42, 46, 50, 47, 49, 48, 52, 44, 45, 51, 56, 53, 54, 55, 58, 60, 61, 57, 59, 62, 63, 64, 67, 69, 68, 71, 65, 66, 70, 72, 77, 74, 75, 76, 73, 78, 79, 81, 82, 80, 83, 84, 85, 88, 91, 90, 86, 87, 89, 92, 99, 93, 98, 94, 97, 95,