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

1,2

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).

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.

Example

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.

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

Crossrefs

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

Sequence in context: A283909 A107385 A342125 * A283846 A321727 A145541

Adjacent sequences: A332318 A332319 A332320 * A332322 A332323 A332324

Keyword

nonn

Author

Amiram Eldar, Feb 09 2020

Status

approved