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 A064273 Permutation of nonnegative integers: a(n) = A013928(A019565(n)). 5
 0, 1, 2, 4, 3, 6, 10, 18, 5, 9, 13, 27, 22, 43, 64, 128, 7, 14, 20, 40, 33, 68, 100, 202, 47, 93, 143, 282, 232, 469, 702, 1404, 8, 16, 25, 48, 39, 79, 119, 235, 56, 110, 167, 333, 278, 553, 832, 1660, 88, 175, 260, 520, 437, 872, 1303, 2609, 608, 1216, 1826, 3649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS From Antti Karttunen, Aug 24 2014: (Start) The original name of the sequence was: "Inverse of sequence A048672 considered as a permutation of the nonnegative integers". However, the real inverse to A048672 is A246353(n) (= a(n)+1), satisfying A246353(A048672(n)) = n for all n. This sequence subtracts one from the terms of A246353 so as to obtain a permutation of nonnegative integers (bijection [0..] --> [0..]). Sequence is obtained when the range of A019565 is compacted so that it becomes surjective, thus the logarithmic scatter plots look very similar. (Same applies to A246353.) Compare also to the plot of A005940. (End) LINKS Antti Karttunen, Table of n, a(n) for n = 0..478 FORMULA From Antti Karttunen, Aug 24 2014: (Start) a(n) = A013928(A019565(n)). a(n) = A246353(n) - 1. (End) PROG (PARI) allocatemem(234567890); default(primelimit, 2^22) uplim_for_13928 = 13123111; v013928 = vector(uplim_for_13928); A013928(n) = v013928[n]; v013928=0; n=1; while((n < uplim_for_13928), if(issquarefree(n), v013928[n+1] = v013928[n]+1, v013928[n+1] = v013928[n]); n++); A019565(n) = {factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ M. F. Hasler A064273(n) = A013928(A019565(n)); for(n=0, 478, write("b064273.txt", n, " ", A064273(n))); \\ Antti Karttunen, Aug 23 2014 (Scheme) (define (A064273 n) (let loop ((n n) (i 1) (p 1)) (cond ((zero? n) (- (A013928 (+ 1 p)) 1)) ((odd? n) (loop (/ (- n 1) 2) (+ 1 i) (* p (A000040 i)))) (else (loop (/ n 2) (+ 1 i) p))))) ;; Antti Karttunen, Aug 23 2014 CROSSREFS One less than A246353. Cf. A000040, A005940, A013928, A019565, A048672. Sequence in context: A216476 A002326 A285493 * A257986 A327743 A232564 Adjacent sequences:  A064270 A064271 A064272 * A064274 A064275 A064276 KEYWORD easy,nonn AUTHOR Howard A. Landman, Sep 23 2001 EXTENSIONS More terms from Carl R. White, Apr 19 2006 Name changed by Antti Karttunen, Aug 23 2014 STATUS approved

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Last modified October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)