A339907 - OEIS

%I #8 Dec 24 2020 21:22:41

%S 3,5,7,11,13,17,19,21,23,29,31,33,37,41,43,47,53,55,57,59,61,65,67,69,

%T 71,73,79,83,89,97,101,103,107,109,113,127,129,131,137,139,141,145,

%U 149,151,157,161,163,167,173,177,179,181,191,193,197,199,201,209,211,217,223,227,229,233,235,239,241,249,251,253,257

%N Odd squarefree numbers k > 1 for which the bigomega(phi(k)) <= bigomega(k-1), where bigomega gives the number of prime divisors, counted with multiplicity.

%C Terms of A003961(A019565(A339906(i))) [or equally, of A019565(2*A339906(i))], for i = 1.., sorted into ascending order.

%C Natural numbers n > 2 that satisfy equation k * phi(n) = n - 1 (for some integer k) all occur in this sequence. Lehmer conjectured that there are no composite solutions.

%H Antti Karttunen, <a href="/A339907/b339907.txt">Table of n, a(n) for n = 1..18526</a>

%H D. H. Lehmer, <a href="http://dx.doi.org/10.1090/s0002-9904-1932-05521-5">On Euler's totient function</a>, Bulletin of the American Mathematical Society, 38 (1932), 745-751.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lehmer&#39;s_totient_problem">Lehmer's totient problem</a>.

%o (PARI) isA339907(n) = ((n>1)&&(n%2)&&issquarefree(n)&&(bigomega(eulerphi(n))<=bigomega(n-1)));

%Y Cf. A339906.

%Y Cf. A065091, A339908 (subsequences).

%Y Cf. also A339817.

%Y Apart from initial 3, a subsequence of A339910.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 21 2020