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

1,2

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

Mathematica

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

Prog

(PARI) isA374198 = A374197;

Crossrefs

Indices of 1's in A374196.

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

Sequence in context: A204879 A326696 A097603 * A362801 A315754 A315755

Adjacent sequences: A374195 A374196 A374197 * A374199 A374200 A374201

Keyword

nonn

Author

Antti Karttunen, Jul 07 2024

Status

approved