A329887 a(0) = 1, a(1) = 2; for n > 1, if n is even, then a(n) = 2*a(n/2), and if n is odd, a(n) = A283980(a((n-1)/2)).

1, 2, 4, 6, 8, 36, 12, 30, 16, 216, 72, 900, 24, 180, 60, 210, 32, 1296, 432, 27000, 144, 5400, 1800, 44100, 48, 1080, 360, 6300, 120, 1260, 420, 2310, 64, 7776, 2592, 810000, 864, 162000, 54000, 9261000, 288, 32400, 10800, 1323000, 3600, 264600, 88200, 5336100, 96, 6480, 2160, 189000, 720, 37800, 12600, 485100, 240

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Formula

a(0) = 1, a(1) = 2; for n > 1, if n is odd, a(n) = A283980(a((n-1)/2)), and if n is even, then a(n) = 2*a(n/2).

a(n) = A108951(A163511(n)).

a(2^n) = 2^(1+n). [And all the terms following after a(2^n) are > 2^(1+n).]

For n >= 1, a(n) = A329886(A054429(n)).

Example

This irregular table can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A283980 to the parent:
                                     1
                                     |
                  ...................2...................
                 4                                       6
       8......../ \........36                 12......../ \........30
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  16      216         72      900         24      180         60       210
etc.
A329886 is the mirror image of the same tree.

Mathematica

{1}~Join~Nest[Append[#1, If[EvenQ@ #2, 2 #1[[#2/2]], (Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2] &[#1[[(#2 - 1)/2]] ]]] & @@ {#, Length@ # + 1} &, {2}, 55] (* Michael De Vlieger, Dec 29 2019 *)

Prog

(PARI)
A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
A329887(n) = if(n<2, 1+n, if(n%2, A283980(A329887(n\2)), 2*A329887(n/2)));

Crossrefs

Permutation of A025487.

Cf. A054429, A108951, A163511, A283980, A329900.

Cf. also A322827, A329886.

Sequence in context: A057809 A135632 A068541 * A108425 A215216 A059569

Adjacent sequences: A329884 A329885 A329886 * A329888 A329889 A329890

Keyword

nonn

Author

Antti Karttunen, Dec 24 2019

Status

approved