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 A332570 #9 Feb 17 2020 09:36:18 %S A332570 2,4,5,6,9,10,12,13,14,15,18,20,21,22,24,25,26,27,28,30,32,33,34,35, %T A332570 36,38,39,40,42,44,45,46,48,50,51,52,54,55,56,58,60,62,63,64,65,66,68, %U A332570 70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,91,92,94,95,96 %N A332570 Numbers that are norm-abundant in Gaussian integers. %C A332570 Numbers k such that N(sigma(k)) > 2*N(k) = 2*k^2, where sigma(k) = A103228(k) + i*A103229(k) is the sum of divisors of k in Gaussian integers (i is the imaginary unit), and N(z) = Re(z)^2 + Im(z)^2 is the norm of the complex number z. %C A332570 The number of terms not exceeding 10^k for k = 1, 2, ... is 6, 70, 711, 7002, 69925, 701081, 7016287, 70074003, 700557394, 7007078826, ... Apparently this sequence has an asymptotic density of ~0.7. %D A332570 Miriam Hausman, On Norm Abundant Gaussian Integers, The Journal of the Indian Mathematical Society, Vol. 49 (1987), pp. 119-123. %D A332570 József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter III, page 120. %H A332570 Amiram Eldar, <a href="/A332570/b332570.txt">Table of n, a(n) for n = 1..10000</a> %H A332570 Robert Spira, <a href="https://doi.org/10.1080/00029890.1961.11989634">The Complex Sum of Divisors</a>, The American Mathematical Monthly, Vol. 68, No. 2 (1961), pp. 120-124. %e A332570 2 is norm-abundant since sigma(2) = 2 + 3*i and N(2 + 3*i) = 2^2 + 3^2 = 13 > 2 * 2^2 = 8. %t A332570 normAbQ[z_] := Abs[DivisorSigma[1, z, GaussianIntegers -> True]]^2 > 2*Abs[z]^2; Select[Range[100], normAbQ] %Y A332570 Cf. A005101, A103228, A103229, A103230, A332320, A332321, A332571, A332572. %K A332570 nonn %O A332570 1,1 %A A332570 _Amiram Eldar_, Feb 16 2020