|
%I #33 Sep 23 2020 02:47:12
%S 1,2,4,8,3,16,32,6,64,128,12,256,9,5,512,1024,24,18,2048,48,4096,8192,
%T 10,16384,27,96,32768,36,192,65536,131072,20,72,262144,384,524288,
%U 1048576,15,54,2097152,7,4194304,144,768,8388608,108,1536,288,16777216,40,33554432,67108864,30
%N Permutation of natural numbers, take the odd bisection of A122111 and divide the largest prime factor out: a(n) = A052126(A122111(2n-1)).
%H Antti Karttunen, <a href="/A243505/b243505.txt">Table of n, a(n) for n = 1..1024</a>
%H Indranil Ghosh, <a href="/A243505/a243505.txt">Python program for computing the sequence</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A052126(A122111((2*n)-1)).
%F a(n) = A122111((2*n)-1) / A105560((2*n)-1).
%F As a composition of related permutations:
%F a(n) = A122111(A064216(n)).
%F a(n) = A241916(A243065(n)).
%F Other identities:
%F For all n >= 2, a(n) = A070003(A244984(n)-1) / A105560((2*n)-1).
%F For all n >= 1, a(A006254(n)) = A000079(n) and a(A007051(n)) = A000040(n).
%F For all n >= 1, A105560(2n-1) divides a(n).
%t A052126[n_] := n/FactorInteger[n][[-1, 1]];
%t A122111[n_] := Product[Prime[Sum[If[j < i, 0, 1], {j, #}]], {i, Max[#]}]&[ Flatten[Table[Table[PrimePi[f[[1]]], {f[[2]]}], {f, FactorInteger[n]}]]];
%t a[n_] := A052126[A122111[2n-1]];
%t Array[a, 60] (* _Jean-François Alcover_, Sep 23 2020 *)
%o (Scheme) (define (A243505 n) (A122111 (A064216 n)))
%Y Inverse: A243506.
%Y Cf. A000040, A000079, A006254, A007051, A052126, A105560.
%Y Related or similar permutations: A122111, A064216, A241916, A243065-A243066, A244981-A244982, A244983-A244984, A244153-A244154.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 25 2014
|
