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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)).

%I A329887 #16 Dec 29 2019 10:35:18
%S A329887 1,2,4,6,8,36,12,30,16,216,72,900,24,180,60,210,32,1296,432,27000,144,
%T A329887 5400,1800,44100,48,1080,360,6300,120,1260,420,2310,64,7776,2592,
%U A329887 810000,864,162000,54000,9261000,288,32400,10800,1323000,3600,264600,88200,5336100,96,6480,2160,189000,720,37800,12600,485100,240
%N 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)).
%H A329887 Antti Karttunen, <a href="/A329887/b329887.txt">Table of n, a(n) for n = 0..8192</a>
%F A329887 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).
%F A329887 a(n) = A108951(A163511(n)).
%F A329887 a(2^n) = 2^(1+n). [And all the terms following after a(2^n) are > 2^(1+n).]
%F A329887 For n >= 1, a(n) = A329886(A054429(n)).
%e A329887 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:
%e A329887                                      1
%e A329887                                      |
%e A329887                   ...................2...................
%e A329887                  4                                       6
%e A329887        8......../ \........36                 12......../ \........30
%e A329887       / \                 / \                 / \                 / \
%e A329887      /   \               /   \               /   \               /   \
%e A329887     /     \             /     \             /     \             /     \
%e A329887   16      216         72      900         24      180         60       210
%e A329887 etc.
%e A329887 A329886 is the mirror image of the same tree.
%t A329887 {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 *)
%o A329887 (PARI)
%o A329887 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
%o A329887 A329887(n) = if(n<2,1+n,if(n%2,A283980(A329887(n\2)),2*A329887(n/2)));
%Y A329887 Permutation of A025487.
%Y A329887 Cf. A054429, A108951, A163511, A283980, A329900.
%Y A329887 Cf. also A322827, A329886.
%K A329887 nonn
%O A329887 0,2
%A A329887 _Antti Karttunen_, Dec 24 2019