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A358208
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(k), where A001065(k) is the sum of the proper divisors of k.
2
1, 2, 3, 4, 5, 6, 8, 13, 10, 9, 12, 11, 7, 14, 15, 18, 16, 17, 20, 107, 21, 22, 24, 25, 191, 197, 27, 26, 28, 30, 33, 32, 35, 34, 36, 29, 38, 433, 39, 40, 42, 523, 577, 44, 45, 31, 677, 46, 48, 50, 23, 49, 52, 51, 54, 56, 55, 63, 43, 58, 37, 57, 53, 60, 66, 61, 62, 70, 68, 64, 65, 69, 71, 75, 80
OFFSET
1,2
COMMENTS
The majority of terms are concentrated just below the line a(n) = n. However, some terms are much larger because the sum of the proper divisors of all previous terms is a prime number. In the first 10000 terms there are twenty-eight fixed points: 4, 5, 6, ..., 2486, 3280, 3292.
Conjecture: the sequence is a permutation of the positive integers.
EXAMPLE
a(7) = 8 as Sum_{k=1..6} A001065(k) = 0 + 1 + 1 + 3 + 1 + 6 = 12, and 8 is the smallest unused number that shares a factor with 12.
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Nov 04 2022
STATUS
approved