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

Author

David James Sycamore, Jul 11 2024

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A002110, A007947, A055932, A374351.

Programs

PARI

\\ See Links section.

Extensions

More terms from Rémy Sigrist, Aug 19 2024