A395360 - OEIS

A395360

Lexicographically earliest infinite sequence of distinct squarefree semiprimes (A006881) with the properties that (a) for all k >= 1, the k-th prime divides exactly k terms, and (b) a semiprime j*k is excluded if both j and k already divide existing terms.

6, 15, 35, 55, 91, 119, 133, 253, 319, 341, 407, 533, 559, 611, 689, 767, 1037, 1139, 1207, 1241, 1343, 1411, 1691, 1843, 1919, 1957, 2033, 2071, 2147, 2921, 3013, 3151, 3197, 3427, 3473, 3611, 3749, 4843, 5017, 5191, 5249, 5539, 5597, 5713, 5771, 6119, 6913, 7037, 7099, 7223, 7409, 7471, 7781, 7967, 8153, 8339

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OFFSET

1,1

COMMENTS

Condition (b) in the definition ensures that every term contains a prime factor that has not appeared earlier in the sequence. This allows the sequence to be constructed by the greedy algorithm, without having to worry about backtracking. If condition (b) is omitted, we get A392373.

LINKS

Scott R. Shannon, Table of n, a(n) for n = 1..10000

EXAMPLE

The first few terms and their prime factors:

6 = (2)*(3)

15 = (3)*(5)

35 = (5)*(7)

55 = (5)*(11)

91 = (7)*(13)

119 = (7)*(17)

133 = (7)*(19)

253 = (11)*(23)