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 A079814 #23 Aug 29 2025 12:23:08 %S A079814 15,21,33,45,63,75,99,105,135,147,165,189,195,225,231,255,273,285,297, %T A079814 315,345,357,363,375,399,405,429,435,441,465,483,495,525,555,561,567, %U A079814 585,609,615,627,645,651,663,675,693,705,735,741,759,765,777,795,819 %N A079814 Odd integers k such that phi(k)/k < 6/Pi^2 where phi = A000010. %C A079814 Since, as Euler proved, the random chance of two integers not having a common prime factor is 6/Pi^2, these are the odd integers that share common factors with an above average fraction of integers. Is it known, or can it be calculated, what portion of odd integers satisfy this condition? (All even numbers qualify; for all multiples of 2, phi(n)/n <= 0.5.) %C A079814 The sequence is closed under multiplication by any odd number. If we include the even numbers, the sequence of primitive terms begins 2, 15, 21, 33, 663, ... . - _Peter Munn_, Apr 11 2021 %H A079814 Charles R Greathouse IV, <a href="/A079814/b079814.txt">Table of n, a(n) for n = 1..10000</a> %e A079814 phi(33)/33 = 20/33 or 0.6060606...; 6/Pi^2 is 0.6079271.... %t A079814 Select[Range[1, 1000, 2], EulerPhi[#]/# < 6/Pi^2 &] (* _Paolo Xausa_, Aug 29 2025 *) %o A079814 (PARI) is(n)=n%2 && eulerphi(n)/n<6/Pi^2 \\ _Charles R Greathouse IV_, Sep 13 2013 %Y A079814 Cf. A000010 (Euler totient function phi(n)), A280877, A280878, A280879. %K A079814 easy,nonn,changed %O A079814 1,1 %A A079814 _Matthew Vandermast_, Feb 19 2003