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 A381740 #10 Mar 06 2025 01:45:17
%S A381740 6,10,14,30,42,66,70,78,102,105,110,114,130,138,154,170,174,182,186,
%T A381740 190,210,222,230,238,246,258,266,282,286,290,310,318,322,330,354,366,
%U A381740 370,374,390,402,406,410,418,426,430,434,438,442,462,470,474,498,506,510
%N A381740 Squarefree numbers k such that k^2 is abundant.
%C A381740 The least odd term is a(105) = 105.
%C A381740 The least term that is coprime to 6 is a(3637276) = 37182145.
%C A381740 If k is a squarefree number that is divisible by 6, 10 or 14, then it is a term. Therefore a lower bound for the asymptotic density of this sequence is 29/(192*zeta(2)) = 0.0918... .
%C A381740 The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 2, 8, 99, 972, 9826, 97610, 979190, 9770801, 97650638, 976893969, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0976... .
%C A381740 If k is a term then any multiple of k that is squarefree is a term. The primitive terms are in A381741.
%H A381740 Amiram Eldar, <a href="/A381740/b381740.txt">Table of n, a(n) for n = 1..10000</a>
%t A381740 Select[Range[600], SquareFreeQ[#] && DivisorSigma[-1, #^2] > 2 &]
%o A381740 (PARI) isok(k) = {my(f = factor(k)); if(!issquarefree(f), 0, prod(i = 1, #f~, f[i,2] *= 2); sigma(f, -1) > 2);}
%Y A381740 Intersection of A005117 and A381738.
%Y A381740 Subsequences: A087248, A381741.
%Y A381740 Cf. A013661.
%K A381740 nonn,easy
%O A381740 1,1
%A A381740 _Amiram Eldar_, Mar 05 2025