This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289272 #21 Jan 02 2019 11:54:33
%S A289272 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 A289272 35,126,105,462,140,630,420,2310,8,22,24,78,36,110,132,390,40,154,120,
%U A289272 546,180,770,660,2730,56,198,168,858,252,990,924,4290,280,1386,840
%N A289272 Inverse to A289271.
%C A289272 a(2^n-1) = A002110(n) for any n >= 0.
%C A289272 a(2^(n-1)) = A000961(n+1) for any n > 0.
%C A289272 A001221(a(n)) = A000120(n) for any n >= 0.
%C A289272 From _Antti Karttunen_, Jan 01 2019: (Start)
%C A289272 A034684(a(n)) = A000961(1+A001511(n)) for any n >= 1. (See also _Rémy Sigrist_'s comment in A289271).
%C A289272 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 A289272 1
%C A289272 |
%C A289272 ...................2...................
%C A289272 3 6
%C A289272 4......../ \........10 12......../ \........30
%C A289272 / \ / \ / \ / \
%C A289272 / \ / \ / \ / \
%C A289272 / \ / \ / \ / \
%C A289272 5 14 15 42 20 70 60 210
%C A289272 7 18 21 66 28 90 84 330 35 126 105 462 140 630 420 2310
%C A289272 etc.
%C A289272 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 A289272 Compare also to trees like A005940 (A163511) and A052330.
%C A289272 (End)
%H A289272 Rémy Sigrist, <a href="/A289272/b289272.txt">Table of n, a(n) for n = 0..10000</a>
%H A289272 Rémy Sigrist, <a href="/A289272/a289272.gp.txt">PARI program for A289272</a>
%H A289272 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A289272 A289271(1) = 0, hence a(0) = 1.
%e A289272 A289271(2) = 1, hence a(1) = 2.
%e A289272 A289271(3) = 2, hence a(2) = 3.
%e A289272 A289271(4) = 4, hence a(4) = 4.
%e A289272 A289271(5) = 8, hence a(8) = 5.
%e A289272 A289271(6) = 3, hence a(3) = 6.
%e A289272 A289271(7) = 16, hence a(16) = 7.
%e A289272 A289271(8) = 32, hence a(32) = 8.
%e A289272 A289271(9) = 64, hence a(64) = 9.
%e A289272 A289271(10) = 5, hence a(5) = 10.
%o A289272 (PARI) See Links section.
%o A289272 (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 A289272 Cf. A000120, A000961, A001221, A002110, A034684, A088860, A278568, A289271 (inverse), A322989, A322990, A322991, A322992.
%Y A289272 Cf. also A005940, A163511, A052330.
%K A289272 nonn,base,look
%O A289272 0,2
%A A289272 _Rémy Sigrist_, Jun 30 2017