A332321 Numbers k that are norm-superabundant in Gaussian integers, i.e., A103230(m)/m^2 < A103230(k)/k^2 for all m < k.

1, 2, 6, 10, 30, 90, 130, 210, 390, 1170, 2730, 5850, 6630, 19890, 46410, 99450, 139230, 192270, 576810, 1345890, 2884050, 4037670, 7883070, 12113010, 20188350, 23649210, 44414370, 49797930, 55181490, 118246050, 149393790, 165544470, 496633410, 746968950, 827722350

Offset: 1

Author

Amiram Eldar, Feb 09 2020

Keywords

• nonn

Comments

Analogous to superabundant numbers (A004394), with the magnitude of the sum of divisors function generalized for Gaussian integers (sqrt(A103230)) instead of the sum of divisors function (A000203).

Examples

			The first 6 terms of A103230 are 1, 13, 16, 41, 80, 208. The corresponding values of A103230(n)/n^2 are 1, 3.25, 1.777..., 2.5625, 3.2, 5.777... and the record values occur at n = 1, 2, 6, the first 3 terms of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..40
• Robert Spira, The Complex Sum of Divisors, The American Mathematical Monthly, Vol. 68, No. 2 (1961), pp. 120-124.

Crossrefs

Cf. A000203, A004394, A103228, A103229, A103230, A279254, A332320.

Programs

Mathematica

r[n_] := Abs[DivisorSigma[1, n, GaussianIntegers -> True]]^2/n^2; rm = 0; seq = {}; Do[r1 = r[n]; If[r1 > rm, rm = r1; AppendTo[seq, n]], {n, 1, 6*10^5}]; seq