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A246353 If n = Sum 2^e_i, e_i distinct, then a(n) = Position of (product prime_{e_i+1}) among squarefree numbers (A005117). 4

%I

%S 1,2,3,5,4,7,11,19,6,10,14,28,23,44,65,129,8,15,21,41,34,69,101,203,

%T 48,94,144,283,233,470,703,1405,9,17,26,49,40,80,120,236,57,111,168,

%U 334,279,554,833,1661,89,176,261,521,438,873,1304,2610,609,1217,1827,3650,3046,6091,9131

%N If n = Sum 2^e_i, e_i distinct, then a(n) = Position of (product prime_{e_i+1}) among squarefree numbers (A005117).

%C This is an inverse function to A048672. Note the indexing: here the domain starts from 0, but the range starts from 1, while in A048672 it is the opposite.

%C Sequence is obtained when the range of A019565 is compacted so that it becomes surjective on N, thus the logarithmic scatter plots look very similar. (Same applies to A064273). Compare also to the plot of A005940.

%H Antti Karttunen, <a href="/A246353/b246353.txt">Table of n, a(n) for n = 0..478</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A013928(1+A019565(n)) = 1 + A013928(A019565(n)).

%F a(n) = A064273(n) + 1.

%F For all n >= 0, A048672(a(n)) = n.

%F For all n >= 1, a(A048672(n)) = n.

%o (PARI)

%o allocatemem(234567890);

%o default(primelimit, 2^22)

%o uplim_for_13928 = 13123111;

%o v013928 = vector(uplim_for_13928); A013928(n) = v013928[n];

%o 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++);

%o A019565(n) = {factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from _M. F. Hasler_

%o A246353(n) = 1+A013928(A019565(n));

%o for(n=0, 478, write("b246353.txt", n, " ", A246353(n)));

%o (Scheme) (definec (A246353 n) (let loop ((n n) (i 1) (p 1)) (cond ((zero? n) (A013928 (+ 1 p))) ((odd? n) (loop (/ (- n 1) 2) (+ 1 i) (* p (A000040 i)))) (else (loop (/ n 2) (+ 1 i) p)))))

%Y Cf. A000040, A005940, A013928, A019565, A048672, A064273.

%K nonn

%O 0,2

%A _Antti Karttunen_, Aug 23 2014

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)