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

476985600, 815673600, 1018886400, 1177862400, 1493049600, 2014214400, 2373638400, 2712326400, 3756614400, 3863865600, 4744454400, 5218617600, 5246841600, 6234681600, 7928121600, 8108755200, 8245036800, 8972409600, 9062726400, 9824774400, 10502150400, 10603756800

Offset: 1

Author

Amiram Eldar, May 05 2025

Keywords

• nonn

Comments

Exponential infinitary abundant numbers are numbers k such that A361175(k) > 2*k.

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.

All the terms are nonsquarefree numbers (A013929), since A361175(k) = k if k is a squarefree number (A005117).

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).

Links

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

Crossrefs

Cf. A005117, A322857, A361175.

Subsequence of A013929 and A129575.

A383696 is a subsequence.

Programs

Mathematica

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 *)

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