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A379030 Nonsquarefree modified exponential abundant numbers: nonsquarefree numbers k such that A241405(k) > 2*k.

%I A379030 #8 Dec 16 2024 02:16:51
%S A379030 120,150,168,270,294,420,630,660,726,750,780,840,924,990,1014,1020,
%T A379030 1050,1092,1140,1170,1320,1380,1386,1428,1470,1530,1560,1596,1638,
%U A379030 1650,1710,1734,1740,1848,1860,1890,1950,2040,2058,2070,2142,2166,2184,2220,2280,2394
%N A379030 Nonsquarefree modified exponential abundant numbers: nonsquarefree numbers k such that A241405(k) > 2*k.
%C A379030 All the squarefree abundant numbers (A087248) are also modified exponential abundant numbers (A379029). This sequence lists the terms of A379029 that are not in A087248.
%C A379030 The numbers of terms that do no exceed 10^k, for k = 3, 4, ..., are 14, 211, 2090, 21236, 212744, 2123071, 21235175, 212450318, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0212... .
%H A379030 Amiram Eldar, <a href="/A379030/b379030.txt">Table of n, a(n) for n = 1..10000</a>
%t A379030 f[p_, e_] := DivisorSum[e + 1, p^(# - 1) &]; mesigma[1] = 1; mesigma[n_] := Times @@ f @@@ FactorInteger[n]; nsmeAbQ[n_] := !SquareFreeQ[n] && mesigma[n] > 2*n; Select[Range[2400], nsmeAbQ]
%o A379030 (PARI) is(n) = {my(f=factor(n)); if(issquarefree(f), 0, prod(i=1, #f~, sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))) > 2*n);}
%Y A379030 Intersection of A013929 and A379029.
%Y A379030 Complement of A087248 within A379029.
%Y A379030 Cf. A005117, A241405.
%K A379030 nonn,easy
%O A379030 1,1
%A A379030 _Amiram Eldar_, Dec 14 2024