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%I #28 Mar 05 2021 21:47:03
%S 1,2,6,4,30,12,36,8,210,60,180,24,900,72,216,16,2310,420,1260,120,
%T 6300,360,1080,48,44100,1800,5400,144,27000,432,1296,32,30030,4620,
%U 13860,840,69300,2520,7560,240,485100,12600,37800,720,189000,2160,6480,96,5336100,88200,264600,3600,1323000,10800,32400,288,9261000
%N 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).
%H Antti Karttunen, <a href="/A329886/b329886.txt">Table of n, a(n) for n = 0..8191</a>
%H Michael De Vlieger, <a href="/A329886/a329886.png">Tree showing levels 0 <= j <= 5</a>
%H Michael De Vlieger, <a href="/A329886/a329886_1.png">Tree showing levels 0 <= j <= 7</a>
%F 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).
%F a(n) = A108951(A005940(1+n)).
%F For n >= 1, a(n) = A329887(A054429(n)).
%e 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:
%e 1
%e |
%e ...................2...................
%e 6 4
%e 30......../ \........12 36......../ \........8
%e / \ / \ / \ / \
%e / \ / \ / \ / \
%e / \ / \ / \ / \
%e 210 60 180 24 900 72 216 16
%e etc.
%e A329887 is the mirror image of the same tree. See also A342000.
%t 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]]
%t (* or, via Doudna *)
%t 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 *)
%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 A329886(n) = if(n<2,1+n,if(!(n%2),A283980(A329886(n/2)),2*A329886(n\2)));
%Y Permutation of A025487.
%Y Cf. A005940, A054429, A108951, A283980, A329900, A342000.
%Y Cf. also A283477, A322827, A329887, A337376/A337377.
%K nonn,look
%O 0,2
%A _Antti Karttunen_, Dec 24 2019
%E Name amended by _Antti Karttunen_, Mar 05 2021
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