A374445 Lexicographically earliest sequence of distinct positive integers such that any pair of consecutive terms are coprime whereas the squarefree kernel of their product is primorial.
1, 2, 3, 4, 9, 8, 15, 14, 45, 16, 27, 10, 21, 20, 63, 40, 81, 32, 75, 28, 135, 56, 165, 98, 225, 64, 105, 22, 315, 44, 525, 88, 735, 128, 243, 50, 147, 80, 189, 100, 231, 130, 693, 160, 441, 110, 273, 220, 567, 200, 729, 70, 33, 140, 99, 280, 297, 350, 363
Offset: 1
Keywords
Examples
The sequence starts with a(1) = 1, a(2) = 2 since (1,2) = 1 and 1*2 = A002110(1). a(3) = 3 since (2,3) = 1 and 2*3 = 6 = A002110(2).
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, PARI program
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..10000, showing primes in red, proper prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and magenta, with magenta representing powerful numbers that are not prime powers.
Programs
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Mathematica
nn = 540; c[_] := False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; j = a[2]; u = 3; f[x_] := f[x] = Or[IntegerQ@ Log2[x], And[EvenQ[x], Union@ Differences@ PrimePi@ FactorInteger[x][[All, 1]] == {1}]]; Monitor[Do[k = u; While[Or[! CoprimeQ[j, k], c[k], ! f[j*k]], k++]; Set[{a[n], c[k], j}, {k, True, k}]; If[k == u, While[c[u], u++]], {n, 3, nn}], n]; Array[a, nn] (* Michael De Vlieger, Jul 16 2024 *) -
PARI
\\ See Links section.
Extensions
More terms from Rémy Sigrist, Jul 11 2024
Comments