A329886 Primorial inflation of Doudna-tree: a(0) = 1, a(1) = 2; for n > 1, if n is even, a(n) = A283980(a(n/2)), and if n is odd, then a(n) = 2*a((n-1)/2).

1, 2, 6, 4, 30, 12, 36, 8, 210, 60, 180, 24, 900, 72, 216, 16, 2310, 420, 1260, 120, 6300, 360, 1080, 48, 44100, 1800, 5400, 144, 27000, 432, 1296, 32, 30030, 4620, 13860, 840, 69300, 2520, 7560, 240, 485100, 12600, 37800, 720, 189000, 2160, 6480, 96, 5336100, 88200, 264600, 3600, 1323000, 10800, 32400, 288, 9261000

Offset: 0

Author

Antti Karttunen, Dec 24 2019

Keywords

• nonn
• look

Examples

			This irregular table can be represented as a binary tree. Each child to the left is obtained by applying A283980 to the parent, and each child to the right is obtained by doubling the parent:
                                     1
                                     |
                  ...................2...................
                 6                                       4
      30......../ \........12                 36......../ \........8
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  210      60         180     24          900      72         216      16
etc.
A329887 is the mirror image of the same tree. See also A342000.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Michael De Vlieger, Tree showing levels 0 <= j <= 5
• Michael De Vlieger, Tree showing levels 0 <= j <= 7

Crossrefs

Permutation of A025487.

Cf. A005940, A054429, A108951, A283980, A329900, A342000.

Cf. also A283477, A322827, A329887, A337376/A337377.

Programs

Mathematica

Block[{a}, a[0] = 1; a[1] = 2; a[n_] := a[n] = If[EvenQ@ n, (Times @@ Map[Prime[PrimePi@#1 + 1]^#2 & @@ # &, FactorInteger[#]] - Boole[# == 1])*2^IntegerExponent[#, 2] &[a[n/2]], 2 a[(n - 1)/2]]; Array[a, 57, 0]]
(* or, via Doudna *)
Map[Times @@ Flatten@ MapIndexed[ConstantArray[Prime[First[#2]], #1] &, Table[LengthWhile[#1, # >= j &], {j, #2}] & @@ {#, Max[#]} &@ Sort[Flatten[ConstantArray[PrimePi@#1, #2] & @@@ FactorInteger[#]], Greater]] &, Nest[Append[#1, Prime[1 + BitLength[#2] - DigitCount[#2, 2, 1]]*#1[[#2 - 2^Floor@ Log2@ #2 + 1]]] & @@ {#, Length@ #} &, {1}, 57] ] (* Michael De Vlieger, Mar 05 2021 *)

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
A329886(n) = if(n<2,1+n,if(!(n%2),A283980(A329886(n/2)),2*A329886(n\2)));

Formula

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

a(n) = A108951(A005940(1+n)).

For n >= 1, a(n) = A329887(A054429(n)).

Extensions

Name amended by Antti Karttunen, Mar 05 2021