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%I #21 Jan 02 2019 11:54:33
%S 1,2,3,6,4,10,12,30,5,14,15,42,20,70,60,210,7,18,21,66,28,90,84,330,
%T 35,126,105,462,140,630,420,2310,8,22,24,78,36,110,132,390,40,154,120,
%U 546,180,770,660,2730,56,198,168,858,252,990,924,4290,280,1386,840
%N Inverse to A289271.
%C a(2^n-1) = A002110(n) for any n >= 0.
%C a(2^(n-1)) = A000961(n+1) for any n > 0.
%C A001221(a(n)) = A000120(n) for any n >= 0.
%C From _Antti Karttunen_, Jan 01 2019: (Start)
%C A034684(a(n)) = A000961(1+A001511(n)) for any n >= 1. (See also _Rémy Sigrist_'s comment in A289271).
%C This sequence can be regarded also as an irregular triangle with rows of lengths 1, 1, 2, 4, 8, 16, ..., that is, it can be represented as a binary tree, where each left hand child contains A322991(k), and each right hand child contains A322992(k), when their parent contains k:
%C 1
%C |
%C ...................2...................
%C 3 6
%C 4......../ \........10 12......../ \........30
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 5 14 15 42 20 70 60 210
%C 7 18 21 66 28 90 84 330 35 126 105 462 140 630 420 2310
%C etc.
%C The leftmost edge is A000961, the next lefmost is A278568 (after 2: 6, 10, 14, 18, ...), the righmost edge is A002110, the next rightmost A088860 but with 3 instead of 4.
%C Compare also to trees like A005940 (A163511) and A052330.
%C (End)
%H Rémy Sigrist, <a href="/A289272/b289272.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A289272/a289272.gp.txt">PARI program for A289272</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A289271(1) = 0, hence a(0) = 1.
%e A289271(2) = 1, hence a(1) = 2.
%e A289271(3) = 2, hence a(2) = 3.
%e A289271(4) = 4, hence a(4) = 4.
%e A289271(5) = 8, hence a(8) = 5.
%e A289271(6) = 3, hence a(3) = 6.
%e A289271(7) = 16, hence a(16) = 7.
%e A289271(8) = 32, hence a(32) = 8.
%e A289271(9) = 64, hence a(64) = 9.
%e A289271(10) = 5, hence a(5) = 10.
%o (PARI) See Links section.
%o (PARI) A289272(n) = { my(m=1, pp=1); while(n>0, pp++; while(!isprimepower(pp)||(gcd(pp,m)>1), pp++); if(n%2, m *= pp); n >>=1); (m); }; \\ _Antti Karttunen_, Jan 01 2019
%Y Cf. A000120, A000961, A001221, A002110, A034684, A088860, A278568, A289271 (inverse), A322989, A322990, A322991, A322992.
%Y Cf. also A005940, A163511, A052330.
%K nonn,base,look
%O 0,2
%A _Rémy Sigrist_, Jun 30 2017
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