A329887 - OEIS

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 #16 Dec 29 2019 10:35:18

%S 1,2,4,6,8,36,12,30,16,216,72,900,24,180,60,210,32,1296,432,27000,144,

%T 5400,1800,44100,48,1080,360,6300,120,1260,420,2310,64,7776,2592,

%U 810000,864,162000,54000,9261000,288,32400,10800,1323000,3600,264600,88200,5336100,96,6480,2160,189000,720,37800,12600,485100,240

%N 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 Antti Karttunen, <a href="/A329887/b329887.txt">Table of n, a(n) for n = 0..8192</a>

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

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

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

%e 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 1

%e |

%e ...................2...................

%e 4 6

%e 8......../ \........36 12......../ \........30

%e / \ / \ / \ / \

%e 16 216 72 900 24 180 60 210

%e etc.

%e A329886 is the mirror image of the same tree.

%t {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 (PARI)

%o 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(n) = if(n<2,1+n,if(n%2,A283980(A329887(n\2)),2*A329887(n/2)));

%Y Permutation of A025487.

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

%Y Cf. also A322827, A329886.

%K nonn

%O 0,2

%A _Antti Karttunen_, Dec 24 2019