A370500 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) does not share a factor with a(n-1) but sopfr(a(n)) does share a factor with soprf(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.

1, 2, 9, 4, 15, 8, 3, 14, 27, 20, 77, 16, 21, 5, 6, 25, 18, 35, 24, 65, 32, 33, 7, 10, 49, 12, 115, 36, 55, 39, 50, 51, 26, 81, 38, 105, 44, 91, 30, 119, 57, 11, 28, 45, 62, 85, 42, 95, 64, 69, 13, 22, 63, 74, 75, 56, 169, 60, 121, 40, 123, 70, 87, 98, 93, 17, 52, 99, 145, 66, 133, 72, 125, 46

Offset

1,2

Comments

The fixed points begin 1, 2, 4, 56, 72, 138, 200, 438, 500, 540, 590, 3998. 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(4) = 4 as a(3) = 9 and 4 does not share a factor with 9 while sopfr(4) = 4 does share a factor with sopfr(9) = 6.

Crossrefs

Cf. A001414, A370501, A370047, A370496, A352588.

Sequence in context: A342663 A332575 A080803 * A339316 A228967 A342661

Adjacent sequences: A370497 A370498 A370499 * A370501 A370502 A370503

Keyword

nonn

Author

Scott R. Shannon, Feb 20 2024

Status

approved