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
FORMULA
PROG
(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
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
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