A363171 Numbers k such that A064549(k) is an abundant number (A005101).

6, 10, 12, 14, 18, 20, 24, 28, 30, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176, 180, 182, 184, 186

Offset: 1

Author

Amiram Eldar, May 19 2023

Keywords

• nonn

Comments

First differs from A334166 at n = 21.

The least odd term is a(33) = 105, and the least term that is coprime to 6 is a(11850456) = 37182145.

The ordered values of A003557(A363169(n)): m is a powerful abundant number (A363169) if and only if A003557(m) is in this sequence.

If k is a term then any positive multiple of k is also a term. The primitive terms are in A363172.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 2, 30, 322, 3201, 31863, 318336, 3188014, 31855257, 318427893, 3184885813, 31853300276, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3185... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003557, A064549, A334166.

Subsequences: A005101, A363169, A363172.

Programs

Mathematica

q[n_] := DivisorSigma[-1, n * Times @@ FactorInteger[n][[;; , 1]]] > 2; Select[Range[200], q]

PARI

A064549(n) = { my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]+1)); };
is(n) = sigma(A064549(n), -1) > 2;