cp's OEIS Frontend

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.

A332320 Numbers k that are highly norm-abundant in Gaussian integers, i.e., A103230(m) < A103230(k) for all m < k.

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%I A332320 #14 Feb 11 2020 03:54:38
%S A332320 1,2,3,4,5,6,10,15,18,20,26,30,50,60,70,78,90,130,150,170,180,210,260,
%T A332320 270,330,390,510,630,780,870,910,990,1020,1050,1110,1170,1530,1890,
%U A332320 1950,2210,2340,2550,2730,3510,4290,4590,5070,5460,5610,5850,6630,8190,10530
%N A332320 Numbers k that are highly norm-abundant in Gaussian integers, i.e., A103230(m) < A103230(k) for all m < k.
%C A332320 Analogous to highly abundant numbers (A002093), with the norm of the sum of divisors function generalized for Gaussian integers (A103230) instead of the sum of divisors function (A000203).
%H A332320 Amiram Eldar, <a href="/A332320/b332320.txt">Table of n, a(n) for n = 1..375</a>
%H A332320 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 A332320 The first 6 terms of A103230 are 1, 13, 16, 41, 80, 208, 64, 113, 169, 1040. The record values occur at n = 1, 2, 3, 4, 5, 6, 10, the first 7 terms of this sequence.
%t A332320 s[n_] := Abs[DivisorSigma[1, n, GaussianIntegers -> True]]^2; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1,10^4}]; seq
%Y A332320 Cf. A000203, A002093, A103228, A103229, A103230, A279254, A332321.
%K A332320 nonn
%O A332320 1,2
%A A332320 _Amiram Eldar_, Feb 09 2020