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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.

%I A298882 #10 Jan 31 2018 06:32:54
%S A298882 1,2,3,4,5,8,7,16,6,32,11,64,13,128,9,256,17,512,19,1024,12,2048,23,
%T A298882 4096,10,8192,18,16384,29,32768,31,65536,24,131072,15,262144,37,
%U A298882 524288,27,1048576,41,2097152,43,4194304,36,8388608,47,16777216,14,33554432,48
%N 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.
%C A298882 This sequence is a permutation of the natural numbers, with inverse A298268.
%C A298882 For any prime p and k > 0:
%C A298882 - if s_p(k) is the k-th p-smooth number and r_p(k) is the k-th p-rough number,
%C A298882 - then a(p * r_p(k)) = p * s_p(k),
%C A298882 - for example: a(11 * A008364(k)) = 11 * A051038(k).
%H A298882 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A298882 a(1) = 1.
%F A298882 a(A083140(n, k)) = A125624(n, k) for any n > 0 and k > 0.
%F A298882 a(n) = A125624(A055396(n), A078898(n)) for any n > 1.
%F A298882 Empirically:
%F A298882 - a(n) = n iff n belongs to A046022,
%F A298882 - a(2 * k) = 2^k for any k > 0,
%F A298882 - a(p^2) = 2 * p for any prime p,
%F A298882 - a(p * q) = 3 * p for any pair of consecutive odd primes (p, q).
%e A298882 The first terms, alongside A020639(n), are:
%e A298882   n     a(n)    lpf(n)
%e A298882   --    ----    ------
%e A298882    1       1      1
%e A298882    2       2      2
%e A298882    3       3      3
%e A298882    4       4      2
%e A298882    5       5      5
%e A298882    6       8      2
%e A298882    7       7      7
%e A298882    8      16      2
%e A298882    9       6      3
%e A298882   10      32      2
%e A298882   11      11     11
%e A298882   12      64      2
%e A298882   13      13     13
%e A298882   14     128      2
%e A298882   15       9      3
%e A298882   16     256      2
%e A298882   17      17     17
%e A298882   18     512      2
%e A298882   19      19     19
%e A298882   20    1024      2
%Y A298882 Cf. A008364, A020639, A046022, A051038, A055396, A078898, A083140, A125624, A298268 (inverse).
%K A298882 nonn
%O A298882 1,2
%A A298882 _Rémy Sigrist_, Jan 28 2018