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URL: https://oeis.org/A392770

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A392770
a(n) is the smallest number not yet in the sequence that has an odd prime factor in common with a(n-2) and a prime factor (either 2 or odd) in common with a(n-1); a(1) = 3, a(2) = 6 (see comments for details).
1
3, 6, 9, 18, 12, 24, 27, 36, 30, 15, 25, 45, 50, 10, 20, 40, 60, 70, 21, 35, 42, 14, 28, 49, 98, 56, 84, 63, 54, 48, 66, 33, 72, 22, 78, 44, 26, 88, 52, 110, 65, 55, 75, 90, 80, 96, 100, 102, 85, 51, 105, 81, 99, 108, 114, 57, 117, 39, 126, 91, 147, 156, 112, 104
OFFSET
1,1
COMMENTS
Aside from the initial term, the numbers in the sequence have to be composite since a(n) has to share one common factor with a(n-1) and another one with a(n-2). In the case the factor is the same, it is counted with multiplicity 2.
EXAMPLE
a(3) = 9 since it has the odd prime factor 3 in common with a(1) = 3 and the odd prime factor 3 in common with a(2) = 6.
a(4) = 18 since it has the odd prime factor 3 in common with a(2) = 6 and the odd prime factor 3 in common with a(3) = 9.
a(5) = 12 since it has the odd prime factor 3 in common with a(3) = 9 and the even prime factor 2 in common with a(4) = 18.
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jan 22 2026
STATUS
approved