cp's OEIS Frontend

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.

A284406 Odd numbers k such that lambda(k) < phi(k) and gcd(lambda(k), k-1) = gcd(phi(k), k-1).

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%I A284406 #31 Jul 14 2020 07:04:17
%S A284406 15,35,39,45,51,55,63,75,85,87,95,99,111,115,117,119,123,135,143,147,
%T A284406 153,155,159,165,171,175,183,187,195,203,205,207,215,219,221,231,235,
%U A284406 245,247,255,259,261,267,275,279,285,287,291,295,299,303,315,319,323,325,327,333,335,339,351
%N A284406 Odd numbers k such that lambda(k) < phi(k) and gcd(lambda(k), k-1) = gcd(phi(k), k-1).
%C A284406 If odd n is in A033949 and n-1 is squarefree, then n is in the sequence.
%C A284406 The set of such numbers has a positive natural density.
%C A284406 The density is 1/2. Almost all odd numbers have this property.
%C A284406 The number of terms below 10^k for k = 1, 2, ... are 0, 12, 204, 2507, 27801, 296583, 3102205, 32054920, 328714616, 3353406273, .... Apparently the asymptotic density of this sequence is less than 1/2. - _Amiram Eldar_, Jul 14 2020
%H A284406 Amiram Eldar, <a href="/A284406/b284406.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..439 from Indranil Ghosh)
%t A284406 Select[Range[1, 351, 2], Function[k, And[#1 < #2, GCD[#1, k - 1] == GCD[#2, k - 1]] & @@ {CarmichaelLambda@ k, EulerPhi@ k}]] (* _Michael De Vlieger_, Mar 26 2017 *)
%Y A284406 Subsequence of A257591.
%Y A284406 A264012 is a subsequence.
%Y A284406 Cf. A000010, A002322, A280262.
%K A284406 nonn
%O A284406 1,1
%A A284406 _Thomas Ordowski_ and _Altug Alkan_, Mar 26 2017