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A370047 a(1) = 1; a(2) = 2; for n > 2, a(n) is smallest unused number such that a(n) shares a factor with a(n-1) and sopfr(a(n)) shares a factor with sopfr(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition. 6
1, 2, 4, 8, 14, 20, 24, 3, 9, 15, 18, 16, 30, 5, 25, 35, 21, 6, 26, 32, 36, 33, 12, 10, 38, 42, 27, 60, 39, 51, 57, 45, 40, 28, 48, 54, 62, 44, 46, 86, 50, 55, 65, 70, 7, 49, 77, 66, 64, 68, 72, 69, 63, 56, 22, 74, 78, 81, 84, 87, 93, 99, 88, 52, 166, 106, 102, 85, 95, 100, 94, 120, 98, 91, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In the first 100000 terms the primes appear in their natural order, although they are delayed relative to similarly sized numbers. In the same range the fixed points are 1, 2, 9, 27, 165, 88812. The sequence is conjectured to be a permutation of the positive numbers.
LINKS
EXAMPLE
a(5) = 14 as a(4) = 8 and 14 is the smallest unused number that shares a factor with 8, while sopfr(14) = 9 shares a factor with sopfr(8) = 6.
CROSSREFS
Sequence in context: A002132 A294065 A248845 * A169926 A140164 A160730
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Feb 08 2024
STATUS
approved

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Last modified May 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)