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

1,1

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

Mathematica

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

Prog

(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;

Crossrefs

Cf. A003557, A064549, A334166.

Subsequences: A005101, A363169, A363172.

Sequence in context: A114989 A362012 A334166 * A336323 A175352 A175397

Adjacent sequences: A363168 A363169 A363170 * A363172 A363173 A363174

Keyword

nonn

Author

Amiram Eldar, May 19 2023

Status

approved