A332320 - OEIS

A332320

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

1, 2, 3, 4, 5, 6, 10, 15, 18, 20, 26, 30, 50, 60, 70, 78, 90, 130, 150, 170, 180, 210, 260, 270, 330, 390, 510, 630, 780, 870, 910, 990, 1020, 1050, 1110, 1170, 1530, 1890, 1950, 2210, 2340, 2550, 2730, 3510, 4290, 4590, 5070, 5460, 5610, 5850, 6630, 8190, 10530

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OFFSET

1,2

COMMENTS

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).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..375

Robert Spira, The Complex Sum of Divisors, The American Mathematical Monthly, Vol. 68, No. 2 (1961), pp. 120-124.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A000203, A002093, A103228, A103229, A103230, A279254, A332321.

Sequence in context: A318533 A048569 A033085 * A349862 A006543 A133745

Adjacent sequences: A332317 A332318 A332319 * A332321 A332322 A332323

KEYWORD

nonn

AUTHOR

Amiram Eldar, Feb 09 2020

STATUS

approved