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 A332572 #7 Feb 17 2020 09:45:19 %S A332572 1,3,7,8,11,16,17,19,23,29,31,37,41,43,47,49,53,57,59,61,67,69,71,73, %T A332572 77,79,83,89,93,97,101,103,107,109,113,121,127,128,129,131,133,137, %U A332572 139,141,149,151,152,157,161,163,167,173,177,179,181,184,191,193,197 %N A332572 Numbers that are norm-deficient in Gaussian integers. %C A332572 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 A332572 The number of terms not exceeding 10^k for k = 1, 2, ... is 4, 30, 289, 2998, 30075, 298919, 2983713, 29925997, 299442606, 2992921174, ... Apparently this sequence has an asymptotic density of ~0.3. %H A332572 Amiram Eldar, <a href="/A332572/b332572.txt">Table of n, a(n) for n = 1..10000</a> %e A332572 3 is norm-deficient since sigma(3) = 4 and N(4) = 4^2 = 16 < 2 * 3^2 = 18. %e A332572 8 is norm-deficient since sigma(8) = -8 - 7*i and N(-8 - 7*i) = (-8)^2 + (-7)^2 = 113 < 2 * 8^2 = 128. %t A332572 normDefQ[z_] := Abs[DivisorSigma[1, z, GaussianIntegers -> True]]^2 < 2*Abs[z]^2; Select[Range[200], normDefQ] %Y A332572 Cf. A005100, A103228, A103229, A103230, A332570. %K A332572 nonn %O A332572 1,2 %A A332572 _Amiram Eldar_, Feb 16 2020