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 A298882 a(1) = 1, and for any n > 1, if n is the k-th number with least prime factor p, then a(n) is the k-th number with greatest prime factor p. 1
 1, 2, 3, 4, 5, 8, 7, 16, 6, 32, 11, 64, 13, 128, 9, 256, 17, 512, 19, 1024, 12, 2048, 23, 4096, 10, 8192, 18, 16384, 29, 32768, 31, 65536, 24, 131072, 15, 262144, 37, 524288, 27, 1048576, 41, 2097152, 43, 4194304, 36, 8388608, 47, 16777216, 14, 33554432, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a permutation of the natural numbers, with inverse A298268. For any prime p and k > 0: - if s_p(k) is the k-th p-smooth number and r_p(k) is the k-th p-rough number, - then a(p * r_p(k)) = p * s_p(k), - for example: a(11 * A008364(k)) = 11 * A051038(k). LINKS FORMULA a(1) = 1. a(A083140(n, k)) = A125624(n, k) for any n > 0 and k > 0. a(n) = A125624(A055396(n), A078898(n)) for any n > 1. Empirically: - a(n) = n iff n belongs to A046022, - a(2 * k) = 2^k for any k > 0, - a(p^2) = 2 * p for any prime p, - a(p * q) = 3 * p for any pair of consecutive odd primes (p, q). EXAMPLE The first terms, alongside A020639(n), are:   n     a(n)    lpf(n)   --    ----    ------    1       1      1    2       2      2    3       3      3    4       4      2    5       5      5    6       8      2    7       7      7    8      16      2    9       6      3   10      32      2   11      11     11   12      64      2   13      13     13   14     128      2   15       9      3   16     256      2   17      17     17   18     512      2   19      19     19   20    1024      2 CROSSREFS Cf. A008364, A020639, A046022, A051038, A055396, A078898, A083140, A125624, A298268 (inverse). Sequence in context: A075162 A056240 A069968 * A086931 A243405 A164339 Adjacent sequences:  A298879 A298880 A298881 * A298883 A298884 A298885 KEYWORD nonn AUTHOR Rémy Sigrist, Jan 28 2018 STATUS approved

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Last modified January 18 10:47 EST 2022. Contains 350454 sequences. (Running on oeis4.)