A370501 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1) but sopfr(a(n)) does not share a factor with soprf(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.

1, 2, 6, 3, 12, 4, 10, 5, 15, 20, 16, 14, 7, 21, 24, 18, 22, 8, 28, 26, 13, 39, 27, 30, 34, 17, 51, 45, 9, 48, 32, 38, 19, 57, 63, 33, 11, 44, 40, 25, 75, 35, 56, 36, 52, 42, 46, 23, 69, 54, 50, 58, 29, 87, 90, 55, 80, 60, 76, 62, 31, 93, 96, 64, 82, 41, 123, 99, 66, 68, 85, 105, 49, 112

Offset

1,2

Comments

The fixed points begin 1, 2, 64, 114, 116, 132, and it is plausible no more exist. The sequence is conjectured to be a permutation of the positive integers.

Links

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

Example

a(6) = 4 as a(5) = 12 and 4 shares a factor with 12 while sopfr(4) = 4 does not share a factor with sopfr(12) = 7.

Crossrefs

Cf. A001414, A370500, A370047, A370496, A352588.

Sequence in context: A298480 A372975 A353916 * A253279 A355212 A297076

Adjacent sequences: A370498 A370499 A370500 * A370502 A370503 A370504

Keyword

nonn

Author

Scott R. Shannon, Feb 20 2024

Status

approved