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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
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, 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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Rémy Sigrist, Aug 19 2024
STATUS
approved