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A374785 Numbers whose unitary divisors have a mean unitary abundancy index that is larger than 2.

%I A374785 #8 Jul 20 2024 14:41:26
%S A374785 223092870,281291010,300690390,6469693230,6915878970,8254436190,
%T A374785 8720021310,9146807670,9592993410,10407767370,10485364890,10555815270,
%U A374785 11125544430,11532931410,11797675890,11823922110,12095513430,12328305990,12598876290,12929686770,13162479330
%N A374785 Numbers whose unitary divisors have a mean unitary abundancy index that is larger than 2.
%C A374785 Numbers k such that A374783(k)/A374784(k) > 2.
%C A374785 The least odd term is A070826(43) = 5.154... * 10^74, and the least term that is coprime to 6 is Product_{k=3..219} prime(k) = 1.0459... * 10^571.
%C A374785 The least nonsquarefree (A013929) term is a(613) = 148802944290 = 2 * 3 * 5 * 7 * 11 * 13 * 17 *19 * 23^2 * 29.
%C A374785 All the terms are nonpowerful numbers (A052485). For powerful numbers (A001694) k, A374783/(k)/A374784(k) < Product_{p prime} (1 + 1/(2*p)) = 1.242534... (A366586).
%H A374785 Amiram Eldar, <a href="/A374785/b374785.txt">Table of n, a(n) for n = 1..1000</a>
%F A374785 A001221(a(n)) >= 9.
%e A374785 223092870 is a term since A374783(223092870)/A374784(223092870) = 666225/330752 = 2.014... > 2.
%t A374785 f[p_, e_] := 1 + 1/(2*p^e); r[1] = 1; r[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[4*10^8], s[#] > 2 &]
%o A374785 (PARI) is(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + 1/(2*f[i,1]^f[i,2])) > 2;}
%Y A374785 Subsequence of A052485.
%Y A374785 Cf. A001221, A001694, A013929, A034683, A070826, A366586, A374783, A374784.
%Y A374785 Similar sequences: A245214, A374788.
%K A374785 nonn
%O A374785 1,1
%A A374785 _Amiram Eldar_, Jul 20 2024