A243505 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A243505

Permutation of natural numbers, take the odd bisection of A122111 and divide the largest prime factor out: a(n) = A052126(A122111(2n-1)).

17

1, 2, 4, 8, 3, 16, 32, 6, 64, 128, 12, 256, 9, 5, 512, 1024, 24, 18, 2048, 48, 4096, 8192, 10, 16384, 27, 96, 32768, 36, 192, 65536, 131072, 20, 72, 262144, 384, 524288, 1048576, 15, 54, 2097152, 7, 4194304, 144, 768, 8388608, 108, 1536, 288, 16777216, 40, 33554432, 67108864, 30

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1024

Indranil Ghosh, Python program for computing the sequence

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A052126(A122111((2*n)-1)).

a(n) = A122111((2*n)-1) / A105560((2*n)-1).

As a composition of related permutations:

a(n) = A122111(A064216(n)).

a(n) = A241916(A243065(n)).

Other identities:

For all n >= 2, a(n) = A070003(A244984(n)-1) / A105560((2*n)-1).

For all n >= 1, a(A006254(n)) = A000079(n) and a(A007051(n)) = A000040(n).

For all n >= 1, A105560(2n-1) divides a(n).

MATHEMATICA

A052126[n_] := n/FactorInteger[n][[-1, 1]];

A122111[n_] := Product[Prime[Sum[If[j < i, 0, 1], {j, #}]], {i, Max[#]}]&[ Flatten[Table[Table[PrimePi[f[[1]]], {f[[2]]}], {f, FactorInteger[n]}]]];

a[n_] := A052126[A122111[2n-1]];

Array[a, 60] (* Jean-François Alcover, Sep 23 2020 *)

PROG

(Scheme) (define (A243505 n) (A122111 (A064216 n)))

CROSSREFS

Inverse: A243506.

Cf. A000040, A000079, A006254, A007051, A052126, A105560.

Related or similar permutations: A122111, A064216, A241916, A243065-A243066, A244981-A244982, A244983-A244984, A244153-A244154.

Sequence in context: A277695 A353709 A317503 * A243065 A352782 A289271

Adjacent sequences: A243502 A243503 A243504 * A243506 A243507 A243508

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 25 2014

STATUS

approved