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.

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

Offset: 1

Author

Scott R. Shannon, Feb 08 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A370496, A370497, A064413, A277272, A027748.