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A358175
a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m.
0
1, 2, 3, 4, 5, 6, 8, 19, 10, 7, 29, 9, 12, 14, 15, 18, 16, 20, 127, 22, 24, 26, 28, 21, 233, 13, 25, 241, 11, 27, 30, 32, 35, 33, 17, 34, 36, 433, 31, 39, 38, 40, 42, 44, 45, 48, 727, 46, 50, 797, 49, 52, 51, 54, 57, 37, 60, 56, 55, 58, 62, 63, 1259, 64, 66, 69, 68, 70, 65, 1579, 72, 78, 77, 74
OFFSET
1,2
COMMENTS
The sequence is conjectured to be a permutation of the positive integers. In the first 10000 terms, other than the first three terms, there are thirty-five fixed points, the last being 2051. It is plausible no more exist although this is unknown.
EXAMPLE
a(9) = 10 as Sum_{k=1..8} A001065(a(k)) = 0 + 1 + 1 + 3 + 1 + 6 + 7 + 1 = 20, and 10 is the smallest unused number that shares a factor with 20.
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Nov 02 2022
STATUS
approved