A363171 - OEIS

%I #8 May 19 2023 06:14:11

%S 6,10,12,14,18,20,24,28,30,36,40,42,44,48,50,52,54,56,60,66,70,72,78,

%T 80,84,88,90,96,98,100,102,104,105,108,110,112,114,120,126,130,132,

%U 136,138,140,144,150,152,154,156,160,162,168,170,174,176,180,182,184,186

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

%C First differs from A334166 at n = 21.

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

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

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

%C 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... .

%H Amiram Eldar, <a href="/A363171/b363171.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI) A064549(n) = { my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]+1)); };

%o is(n) = sigma(A064549(n), -1) > 2;

%Y Cf. A003557, A064549, A334166.

%Y Subsequences: A005101, A363169, A363172.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 19 2023