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 A381822 #10 Mar 09 2025 12:27:55 %S A381822 1,3,5,7,9,11,13,15,17,19,21,23,25,29,31,33,35,37,39,41,43,45,47,49, %T A381822 51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,83,85,87,89,91,93,95,97, %U A381822 99,101,103,105,107,109,111,113,115,117,119,121,123,127,129,131 %N A381822 Odd cubefree numbers: odd numbers that are not divisible by any cube greater than 1. %C A381822 Numbers whose prime factorization has only odd primes, and all its exponents are smaller than 3 (except for 1 whose prime factorization is empty). %C A381822 The asymptotic density of this sequence is 4/(7*zeta(3)) = 1/(2*A233091) = 0.475375641474689982104... . %C A381822 In general, the asymptotic density of odd k-free numbers (numbers that are not divisible by a k-th power other than 1, k >= 2) is 2^(k-1)/((2^k-1) * zeta(k)). %H A381822 Amiram Eldar, <a href="/A381822/b381822.txt">Table of n, a(n) for n = 1..10000</a> %t A381822 cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;;, 2]], # < 3 &]; Select[Range[1, 150, 2], cubeFreeQ] %o A381822 (PARI) isok(k) = k % 2 && if(k == 1, 1, vecmax(factor(k)[, 2]) < 3); %Y A381822 Intersection of A005408 and A004709. %Y A381822 A056911 is a subsequence. %Y A381822 Cf. A002117, A233091. %K A381822 nonn,easy %O A381822 1,2 %A A381822 _Amiram Eldar_, Mar 08 2025