A374575 Lexicographically earliest infinite sequence of distinct positive integers having the property that for any triple i,j,k of consecutive terms gcd(j,k) = 1 whereas A007947(i*j*k) is a term in A002110.

1, 2, 3, 4, 5, 6, 7, 10, 9, 8, 15, 14, 11, 30, 49, 12, 25, 16, 21, 20, 27, 28, 45, 22, 35, 18, 55, 42, 13, 110, 63, 26, 165, 56, 33, 40, 77, 24, 65, 154, 39, 50, 231, 32, 75, 64, 81, 70, 99, 52, 105, 44, 91, 60, 121, 84, 125, 36, 175, 48, 143, 140, 51, 286

Offset

1,2

Comments

In other words a(n) is least k such that (j,k) = 1 and rad(i*j*k) is a primorial number (alternatively i*j*k is a term in A055932).

Conjectured to be a permutation of the positive integers with primes in order.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..10^4, showing primes in red, proper prime powers in yellow, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and magenta, with magenta signifying powerful numbers that are not prime powers.

Rémy Sigrist, PARI program

Example

Sequence starts with a(1,2,3) = {1,2,3} because this is the smallest consecutive triple of terms satisfying the definition ((2,3) = 1 and rad(1*2*3) = 6 = A002110(2)).
a(4) = 4 because (3,4) = 1, rad(2*3*4) = 6 = A002110(2), and 4 is the smallest unused number with this property.

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A002110, A007947, A055932, A374351.

Sequence in context: A372368 A266646 A364280 * A361810 A362854 A102455

Adjacent sequences: A374572 A374573 A374574 * A374576 A374577 A374578

Keyword

nonn

Author

David James Sycamore, Jul 11 2024

Extensions

More terms from Rémy Sigrist, Aug 19 2024

Status

approved