A329886 - OEIS

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

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

OFFSET

0,2

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

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)).

EXAMPLE

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:

...................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.

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 *)

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

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

CROSSREFS

Permutation of A025487.

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

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

Sequence in context: A228099 A227955 A324922 * A064538 A002790 A108951

Adjacent sequences: A329883 A329884 A329885 * A329887 A329888 A329889

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Dec 24 2019

EXTENSIONS

Name amended by Antti Karttunen, Mar 05 2021

STATUS

approved