cp's OEIS Frontend

A357686 Nonsquarefree numbers k such that A293228(k) > k.

%I A357686 #9 Oct 12 2022 04:31:47
%S A357686 60,84,132,140,156,204,228,276,348,372,420,444,492,516,564,636,660,
%T A357686 708,732,780,804,852,876,924,948,996,1020,1068,1092,1140,1164,1212,
%U A357686 1236,1284,1308,1356,1380,1428,1524,1540,1572,1596,1644,1668,1716,1740,1788,1812,1820
%N A357686 Nonsquarefree numbers k such that A293228(k) > k.
%C A357686 The squarefree numbers k such that A293228(k) > k are the squarefree abundant numbers (A087248).
%C A357686 If k > 3 is a term of A243128 then 4*k is a term.
%C A357686 The least odd term is (3/2)*prime(17)# = 2884140525231318958605.
%C A357686 The least term that is coprime to 6 is (5/6)*prime(1245)# = 5.629...*10^4361.
%C A357686 The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 2, 26, 287, 2725, 27660, 275298, 2754638, 27556849, 275538900, 2755151247, ... . Apparently, the asymptotic density of this sequence exists and equals 0.02755... .
%H A357686 Amiram Eldar, <a href="/A357686/b357686.txt">Table of n, a(n) for n = 1..10000</a>
%e A357686 60 = 2^2 * 15 is a term since it is nonsquarefree, its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15, 30} and their sum is 72 > 60.
%t A357686 q[n_] := AnyTrue[(f = FactorInteger[n])[[;;, 2]], # > 1 &] && Times @@ (1 + f[[;; , 1]]) > n; Select[Range[2, 2000], q]
%o A357686 (PARI) is(n) = {my(f = factor(n)); if(n == 1 || vecmax(f[,2]) == 1, return(0)); prod(i=1, #f~, f[i,1]+1) > n};
%Y A357686 Intersection of A013929 and A357685.
%Y A357686 Subsequence of A005101.
%Y A357686 Cf. A087248, A243128.
%K A357686 nonn
%O A357686 1,1
%A A357686 _Amiram Eldar_, Oct 09 2022