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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
 1, 2, 3, 5, 4, 7, 11, 19, 6, 10, 14, 28, 23, 44, 65, 129, 8, 15, 21, 41, 34, 69, 101, 203, 48, 94, 144, 283, 233, 470, 703, 1405, 9, 17, 26, 49, 40, 80, 120, 236, 57, 111, 168, 334, 279, 554, 833, 1661, 89, 176, 261, 521, 438, 873, 1304, 2610, 609, 1217, 1827, 3650, 3046, 6091, 9131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. 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. LINKS Antti Karttunen, Table of n, a(n) for n = 0..478 FORMULA a(n) = A013928(1+A019565(n)) = 1 + A013928(A019565(n)). a(n) = A064273(n) + 1. For all n >= 0, A048672(a(n)) = n. For all n >= 1, a(A048672(n)) = n. 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]])~))}; \\ This function from M. F. Hasler A246353(n) = 1+A013928(A019565(n)); for(n=0, 478, write("b246353.txt", n, " ", A246353(n))); (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))))) CROSSREFS Cf. A000040, A005940, A013928, A019565, A048672, A064273. Sequence in context: A329821 A259153 A028691 * A194009 A242388 A257985 Adjacent sequences:  A246350 A246351 A246352 * A246354 A246355 A246356 KEYWORD nonn AUTHOR Antti Karttunen, Aug 23 2014 STATUS approved

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Last modified August 6 10:01 EDT 2020. Contains 336245 sequences. (Running on oeis4.)