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A064273
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Permutation of nonnegative integers: a(n) = A013928(A019565(n)).
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5
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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
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OFFSET
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0,3
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COMMENTS
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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)
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LINKS
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FORMULA
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(End)
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PROG
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(PARI)
allocatemem(234567890);
default(primelimit, 2^22)
uplim_for_13928 = 13123111;
v013928 = vector(uplim_for_13928); A013928(n) = v013928[n];
v013928[1]=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
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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