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

1,1

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.

Links

Hal M. Switkay, Table of n, a(n) for n = 1..82

D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.

Example

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.

Crossrefs

Cf. A002110, A025487, A036913.

Sequence in context: A348412 A133996 A284573 * A080742 A005417 A058215

Adjacent sequences: A355472 A355473 A355474 * A355476 A355477 A355478

Keyword

nonn

Author

Hal M. Switkay, Jul 03 2022

Status

approved