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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 Scott R. Shannon, Table of n, a(n) for n = 1..10000 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 Cf. A001414, A370496, A370497, A064413, A277272, A027748. Sequence in context: A002132 A294065 A248845 * A169926 A140164 A160730 Adjacent sequences: A370044 A370045 A370046 * A370048 A370049 A370050 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.)