A374198 After initial 1, numbers k such that at least one of their divisors is a multiply-perfect number (A007691) larger than one.

1, 6, 12, 18, 24, 28, 30, 36, 42, 48, 54, 56, 60, 66, 72, 78, 84, 90, 96, 102, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 162, 168, 174, 180, 186, 192, 196, 198, 204, 210, 216, 222, 224, 228, 234, 240, 246, 252, 258, 264, 270, 276, 280, 282, 288, 294, 300, 306, 308, 312, 318, 324, 330, 336, 342, 348, 354, 360

Offset: 1

Author

Antti Karttunen, Jul 07 2024

Keywords

• nonn

Comments

A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

The asymptotic density of this sequence is Sum_{s subset of A007691 \ {1}} (-1)^(card(s)+1)/LCM(s) = 0.1916963... . - Amiram Eldar, Apr 16 2025

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20001

Crossrefs

Indices of 1's in A374196.

Cf. A007691, A097603 (essentially the same), A374197 (characteristic function).

Programs

Mathematica

q[n_] := n == 1 || AnyTrue[Rest[Divisors[n]], IntegerQ[DivisorSigma[-1, #]] &]; Select[Range[360], q] (* Amiram Eldar, Apr 16 2025 *)

PARI

isA374198 = A374197;