A355475 Numbers that are sparsely totient (A036913) and of least prime signature (A025487).

2, 6, 12, 30, 60, 120, 210, 240, 420, 840, 1260, 1680, 2310, 4620, 9240, 13860, 18480, 30030, 60060, 120120, 180180, 240240, 360360, 510510, 1021020, 2042040, 3063060, 4084080, 6126120, 8168160, 9699690, 12252240, 19399380, 38798760, 58198140, 77597520

Offset: 1

Author

Hal M. Switkay, Jul 03 2022

Keywords

• nonn

Comments

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

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

Examples

			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.
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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..141 (terms 1..82 from Hal M. Switkay)
• D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.

Crossrefs

Cf. A002110, A025487, A036913.