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 A383031 #6 Apr 13 2025 16:32:37
%S A383031 1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,19,21,22,23,25,26,27,28,29,
%T A383031 30,32,33,34,35,36,37,38,40,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
%U A383031 56,57,58,59,60,61,62,64,65,66,67,68,70,71,72,73,75,76,77,78
%N A383031 Indices of the squarefree terms in the sequence of exponentially odd numbers.
%C A383031 The asymptotic density of this sequence is A059956/A065463 = Product_{p prime} (1 - 1/(p^3 + p^2 - p)) = 0.86299074784... .
%H A383031 Amiram Eldar, <a href="/A383031/b383031.txt">Table of n, a(n) for n = 1..10000</a>
%F A383031 A268335(a(n)) = A005117(n).
%t A383031 expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; Position[Select[Range[120], expOddQ], _?SquareFreeQ, Heads -> False] // Flatten
%o A383031 (PARI) isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if(!(f[i, 2] % 2), return (0))); 1; }
%o A383031 list(lim) = {my(c = 0); for(k = 1, lim, if(isexpodd(k), c++; if(issquarefree(k), print1(c, ", ")))); }
%Y A383031 Cf. A005117, A059956, A065463, A268335, A383030.
%K A383031 nonn,easy
%O A383031 1,2
%A A383031 _Amiram Eldar_, Apr 13 2025