%I #20 Jul 28 2024 10:07:58

%S 2,6,12,30,60,120,210,240,420,840,1260,1680,2310,4620,9240,13860,

%T 18480,30030,60060,120120,180180,240240,360360,510510,1021020,2042040,

%U 3063060,4084080,6126120,8168160,9699690,12252240,19399380,38798760,58198140,77597520

%N Numbers that are sparsely totient (A036913) and of least prime signature (A025487).

%C All sparsely totient numbers are even, but not all sparsely totient numbers have least prime signature.

%C The present sequence is infinite, as it includes all primorials greater than one (A002110); see Masser and Shiu for proof.

%H Amiram Eldar, <a href="/A355475/b355475.txt">Table of n, a(n) for n = 1..141</a> (terms 1..82 from Hal M. Switkay)

%H D. W. Masser and P. Shiu, <a href="https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-121/issue-2/On-sparsely-totient-numbers/pjm/1102702441.full">On sparsely totient numbers</a>, Pacific J. Math. 121, no. 2 (1986), 407-426.

%e The totient of 18 is 6, which is smaller than the totient of all larger natural numbers; but 18 does not have least prime signature, so it is not a term of this sequence.

%e The totient of 30 is 8, which is smaller than the totient of all larger natural numbers; since 30 has least prime signature, it is a term of this sequence.

%Y Cf. A002110, A025487, A036913.

%K nonn

%O 1,1

%A _Hal M. Switkay_, Jul 03 2022