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 A337377 #27 Jul 08 2021 14:22:10
%S A337377 1,1,2,1,3,1,4,1,5,3,2,1,9,2,8,1,7,5,10,3,3,1,4,1,25,9,6,1,27,4,16,1,
%T A337377 11,7,14,5,21,5,20,3,5,3,2,1,9,2,8,1,49,25,50,9,15,3,4,1,125,27,18,2,
%U A337377 81,8,32,1,13,11,22,7,33,7,28,5,55,21,14,5,63,10,40,3,7,5,10,3,3,1,4,1,25,9,6,1,27,4,16,1,121
%N A337377 Primorial deflation (denominator) of Doudna-tree.
%C A337377 Like A005940, also this irregular table can be represented as a binary tree:
%C A337377 1
%C A337377 |
%C A337377 ...................1...................
%C A337377 2 1
%C A337377 3......../ \........1 4......../ \........1
%C A337377 / \ / \ / \ / \
%C A337377 / \ / \ / \ / \
%C A337377 / \ / \ / \ / \
%C A337377 5 3 2 1 9 2 8 1
%C A337377 7 5 10 3 3 1 4 1 25 9 6 1 27 4 16 1
%C A337377 etc.
%C A337377 A194602 gives the positions of nodes that have value 1. They correspond to terms of A005940 that are products of primorials (A025487). The first 2^k nodes contain A000041(k+1) 1's.
%C A337377 a(n) is even if and only if A005940(1+n) occurs in A277569.
%H A337377 Antti Karttunen, <a href="/A337377/b337377.txt">Table of n, a(n) for n = 0..8191</a>
%H A337377 Antti Karttunen, <a href="/A337377/a337377.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A337377 <a href="/index/Fo#fraction_trees">Index entries for fraction trees</a>
%F A337377 a(n) = A319627(A005940(1+n)).
%F A337377 For n >= 1, a(2*n) = A003961(a(n)) * A006519(n+1).
%F A337377 a(2*n+1) = A026741(a(n)).
%t A337377 Array[#2/GCD[#1, #2] & @@ {#, Apply[Times, Map[If[#1 <= 2, 1, NextPrime[#1, -1]]^#2 & @@ # &, FactorInteger[#]]]} &@ Function[p, Times @@ Flatten@ Table[Prime[Count[Flatten[#], 0] + 1]^#[[1, 1]] &@ Take[p, -i], {i, Length[p]}]]@ Partition[Split[Join[IntegerDigits[# - 1, 2], {2}]], 2] &[# + 1] &, 96] (* _Michael De Vlieger_, Aug 27 2020 *)
%o A337377 (PARI)
%o A337377 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A337377 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A337377 A319627(n) = (A064989(n) / gcd(n, A064989(n)));
%o A337377 A337377(n) = A319627(A005940(1+n));
%Y A337377 Cf. A337376 (numerators).
%Y A337377 A003961, A005940, A006519, A026741, A064989, A319627 are used in a formula defining this sequence.
%Y A337377 Cf. A000041, A025487, A277569.
%Y A337377 Positions of 1's: A194602.
%Y A337377 Cf. also A329886, A346097.
%K A337377 nonn,frac,look
%O A337377 0,3
%A A337377 _Antti Karttunen_, _Michael De Vlieger_ and _Peter Munn_, Aug 25 2020