cp's OEIS Frontend

A383695 Exponential infinitary abundant numbers that are not exponential unitary abundant: numbers k such that A361175(k) > 2*k >= A322857(k).

%I A383695 #10 May 07 2025 10:50:08
%S A383695 476985600,815673600,1018886400,1177862400,1493049600,2014214400,
%T A383695 2373638400,2712326400,3756614400,3863865600,4744454400,5218617600,
%U A383695 5246841600,6234681600,7928121600,8108755200,8245036800,8972409600,9062726400,9824774400,10502150400,10603756800
%N A383695 Exponential infinitary abundant numbers that are not exponential unitary abundant: numbers k such that A361175(k) > 2*k >= A322857(k).
%C A383695 Exponential infinitary abundant numbers are numbers k such that A361175(k) > 2*k.
%C A383695 All the exponential unitary abundant numbers (A383693) are also exponential infinitary abundant numbers. There are numbers that are exponential infinitary abundant and not exponential unitary abundant. The least is: a(1) = 476985600, which is the 427970th exponential infinitary abundant number.
%C A383695 All the terms are nonsquarefree numbers (A013929), since A361175(k) = k if k is a squarefree number (A005117).
%C A383695 The asymptotic density of this sequence is Sum_{n>=1} f(A383696(n)) = 1.9875...*10^(-9), where f(n) = (6/(Pi^2*n))*Product_{prime p|n}(p/(p+1)). The relative density of this sequence within the exponential infinitary abundant numbers is 2.215... * 10^(-6).
%H A383695 Amiram Eldar, <a href="/A383695/b383695.txt">Table of n, a(n) for n = 1..10000</a>
%t A383695 seq[max_] := Module[{prim = seqA383696[max], s = {}, sq}, Do[sq = Select[Range[Floor[max/p]], CoprimeQ[p, #] && SquareFreeQ[#] &]; s = Join[s, p*sq], {p, prim}]; Union[s]]; seq[10^10] (* using the function seqA383696 from A383696 *)
%o A383695 (PARI) list(lim) = {my(p = listA383696(lim), s = []); for(i = 1, #p, s = concat(s, apply(x -> p[i]*x, select(x -> gcd(x, p[i]) == 1 && issquarefree(x), vector(lim\p[i], j, j))))); Set(s);} \\ using the function listA383696 from A383696
%Y A383695 Cf. A005117, A322857, A361175.
%Y A383695 Subsequence of A013929 and A129575.
%Y A383695 A383696 is a subsequence.
%K A383695 nonn
%O A383695 1,1
%A A383695 _Amiram Eldar_, May 05 2025