This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379029 #9 Dec 16 2024 02:17:21
%S A379029 30,42,66,70,78,102,114,120,138,150,168,174,186,210,222,246,258,270,
%T A379029 282,294,318,330,354,366,390,402,420,426,438,462,474,498,510,534,546,
%U A379029 570,582,606,618,630,642,654,660,678,690,714,726,750,762,770,780,786,798,822
%N A379029 Modified exponential abundant numbers: numbers k such that A241405(k) > 2*k.
%C A379029 All the squarefree abundant numbers (A087248) are terms since A241405(k) = A000203(k) for a squarefree number k.
%C A379029 If k is a term and m is coprime to k them k*m is also a term.
%C A379029 The numbers of terms that do no exceed 10^k, for k = 2, 3, ..., are 5, 67, 767, 7595, 76581, 764321, 7644328, 76468851, 764630276, ... . Apparently, the asymptotic density of this sequence exists and equals 0.07646... .
%H A379029 Amiram Eldar, <a href="/A379029/b379029.txt">Table of n, a(n) for n = 1..10000</a>
%t A379029 f[p_, e_] := DivisorSum[e + 1, p^(# - 1) &]; mesigma[1] = 1; mesigma[n_] := Times @@ f @@@ FactorInteger[n]; meAbQ[n_] := mesigma[n] > 2*n; Select[Range[1000], meAbQ]
%o A379029 (PARI) is(n) = {my(f=factor(n)); prod(i=1, #f~, sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))) > 2*n;}
%Y A379029 Cf. A000203, A241405, A323757, A323758, A323759, A379027.
%Y A379029 Subsequence of A005101.
%Y A379029 Subsequences: A034683, A087248, A379030, A379031.
%Y A379029 Similar sequences: A064597, A129575, A129656, A292982, A348274, A348604.
%K A379029 nonn,easy
%O A379029 1,1
%A A379029 _Amiram Eldar_, Dec 14 2024