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.

A276980 Odd squarefree numbers n > 1 such that lambda(n)^2 = phi(n), where lambda is the Carmichael lambda function and phi is Euler's totient function.

This page as a plain text file.
%I A276980 #31 May 03 2017 21:47:44
%S A276980 273,1729,2109,2255,4433,4641,4697,5673,6643,6935,7667,8103,8729,
%T A276980 10235,11543,14497,16385,16523,17507,18915,20033,22649,23579,26691,
%U A276980 29309,29393,34799,35853,35929,37209,37829,39277,42653,45551,55699,56163,68735,68901,69167,69977,70993,73505,75361,76373
%N A276980 Odd squarefree numbers n > 1 such that lambda(n)^2 = phi(n), where lambda is the Carmichael lambda function and phi is Euler's totient function.
%C A276980 Such a number n must have at least three prime factors.
%C A276980 Are there infinitely many such numbers?
%C A276980 Among them are some Carmichael numbers: 1729, 75361, ... (A002997).
%H A276980 Robert G. Wilson v, <a href="/A276980/b276980.txt">Table of n, a(n) for n = 1..1024</a>
%e A276980 273 = 3 * 7 * 13, so phi(273) = 2 * 6 * 12 = 144 = 12^2 and lambda(273) = lcm(2, 6, 12) = 12, hence 273 is in the sequence.
%e A276980 Notice that phi(315) = 144 and lambda(315) = 12 also. However, mu(315) = 0 since 315 = 3^2 * 5 * 7, so for that reason 315 is not in the sequence.
%t A276980 samePsiSqPhiQ[n_] := SquareFreeQ[n] && CarmichaelLambda[n]^2 == EulerPhi[n]; Select[1 + 2 Range@50000, samePsiSqPhiQ] (* _Robert G. Wilson v_, Apr 14 2017 *)
%o A276980 (PARI) is(n) = n>1 && n%2!=0 && issquarefree(n) && lcm(znstar(n)[2])^2==eulerphi(n) \\ _Felix Fröhlich_, Apr 22 2017
%Y A276980 Subsequence of A024556.
%Y A276980 Cf. A000010, A002322, A002997.
%K A276980 nonn
%O A276980 1,1
%A A276980 _Thomas Ordowski_ and _Altug Alkan_, Apr 11 2017