A230761 Indices k where the sum over k-th powers of the integers in a k X k square in the Gaussian plane (A230308) is not == 0 (mod k).

24, 48, 96, 120, 168, 192, 240, 264, 312, 336, 384, 408, 456, 480, 528, 552, 600, 624, 672, 696, 744, 768, 816, 840, 888, 912, 960, 984, 1008, 1032, 1056, 1104, 1128, 1176, 1200, 1248, 1272, 1320, 1344, 1392, 1416, 1464

Offset

1,1

Comments

Define S(k) = Sum_{0<=a<k; 0<=b<k} (a+i*b)^k, where i is the imaginary unit. The sequence contains the places k where S(k) <> 0 (mod k).

Almost the same as A073763, but contains also 1008 (equivalent to A230310(1)), for example.

The asymptotic density of this sequence is 0.028999... (Fortuny Ayuso et al., 2014). - Amiram Eldar, May 01 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..300

Pedro Fortuny Ayuso, Jose Maria Grau and Antonio Oller-Marcen, A von Staudt-type formula for Sum_{z in Zn[i]} z^k, arXiv:1402.0333 [math.NT], 2014.

Crossrefs

The complement of A230308.

Cf. A073763, A230309, A230310.

Sequence in context: A174906 A029613 A083541 * A073763 A359750 A292834

Adjacent sequences: A230758 A230759 A230760 * A230762 A230763 A230764

Keyword

nonn

Author

Jose Maria Grau Ribas, Oct 16 2013

Status

approved