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 A285575 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p. 2
 1, 36, 2, 18, 4, 9, 8, 25, 12, 3, 24, 6, 30, 10, 20, 5, 40, 15, 45, 16, 27, 28, 7, 56, 14, 42, 21, 48, 33, 44, 11, 72, 13, 52, 26, 50, 22, 54, 32, 49, 60, 35, 63, 64, 75, 39, 78, 66, 84, 51, 68, 17, 100, 19, 76, 38, 90, 34, 98, 46, 92, 23, 108, 29, 116, 58 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576). For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have: - c_0 = A000027 (the natural numbers), - c_1 = A285296, - c_2 = a (this sequence). For any k>=0, c_k is a permutation of the natural numbers. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A285575 EXAMPLE The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are: n       a(n)    p --      ----    ---- 1       1       2, 3 2       36      2, 3 3       2       2, 3 4       18      2, 3 5       4       2, 3 6       9       2, 3 7       8       2,    5 8       25      2,    5 9       12      2, 3 10      3       2, 3 11      24      2, 3 12      6       2, 3 13      30      2,    5 14      10      2,    5 15      20      2,    5 16      5       2,    5 17      40      2,    5 18      15         3, 5 19      45      2, 3 20      16      2, 3 ... 115     160     2,    5 116     115     2, 3, 5 117     180     2, 3 ... CROSSREFS Cf. A285296, A285576 (inverse). Sequence in context: A330084 A037935 A159824 * A227168 A100252 A020340 Adjacent sequences:  A285572 A285573 A285574 * A285576 A285577 A285578 KEYWORD nonn,look AUTHOR Rémy Sigrist, Apr 22 2017 STATUS approved

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)