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 A243287 a(1)=1, and for n > 1, if n is k-th number divisible by the square of its largest prime factor (i.e., n = A070003(k)), a(n) = 1 + (2*a(k)); otherwise, when n = A102750(k), a(n) = 2*a(k). 15
 1, 2, 4, 3, 8, 6, 16, 5, 9, 12, 32, 10, 18, 24, 64, 7, 20, 17, 36, 48, 128, 14, 40, 34, 13, 72, 33, 96, 256, 28, 80, 11, 68, 26, 144, 19, 66, 192, 512, 56, 160, 22, 136, 52, 288, 38, 132, 384, 25, 65, 1024, 112, 320, 21, 44, 272, 104, 576, 76, 264, 768, 50, 130, 37, 2048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is an instance of "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case complementary pair A070003/A102750 (numbers which are divisible/not divisible by the square of their largest prime factor) is entangled with complementary pair odd/even numbers (A005408/A005843). Thus this shares with the permutation A122111 the property that each term of A102750 is mapped to a unique even number and likewise each term of A070003 is mapped to a unique odd number. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 1, and thereafter, if A241917(n) = 0 (i.e., n is a term of A070003), a(n) = 1 + (2*a(A243282(n))); otherwise a(n) = 2*a(A243285(n)) (where A243282 and A243285 give the number of integers <= n divisible/not divisible by the square of their largest prime factor). PROG (Scheme, with Antti Karttunen's IntSeq-library) (definec (A243287 n) (cond ((<= n 1) n) ((zero? (A241917 n)) (+ 1 (* 2 (A243287 (A243282 n))))) (else (* 2 (A243287 (A243285 n)))))) CROSSREFS Inverse: A243288. Cf. A005843, A005408, A070003, A102750, A243282, A243285, A241917, A122111. Similarly constructed permutations: A243343-A243346, A135141-A227413, A237126-A237427, A193231. Sequence in context: A243073 A243345 A297499 * A243288 A279352 A279351 Adjacent sequences:  A243284 A243285 A243286 * A243288 A243289 A243290 KEYWORD nonn,look AUTHOR Antti Karttunen, Jun 02 2014 STATUS approved

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Last modified August 14 19:47 EDT 2020. Contains 336483 sequences. (Running on oeis4.)