A335853 Numbers that are highly powerful in Gaussian integers.

1, 2, 4, 8, 16, 32, 64, 100, 200, 400, 500, 800, 1000, 2000, 4000, 5000, 8000, 10000, 18000, 20000, 27000, 36000, 40000, 50000, 54000, 80000, 90000, 108000, 135000, 180000, 216000, 270000, 450000, 540000, 810000, 1080000, 1350000, 1620000, 2160000, 2700000

Offset

1,2

Comments

Numbers with a record value of the product of the exponents in the prime factorization in Gaussian integers (A335852). Equivalently, numbers with a record number of powerful divisors in Gaussian integers.

The corresponding record values are 1, 2, 4, 6, 8, 10, 12, 16, 24, 32, 36, 40, 54, 72, 90, 96, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..81

Amiram Eldar, Table of n, a(n), A335852(a(n)) for n = 1..81

Example

The factorization of 1, 2, 3 and 4 in Gaussian integers are 1, -i*(1+i)^2, 3 and -(1+i)^4, and the corresponding products of the exponents are 1, 2, 1 and 4. The record values, 1, 2 and 4, occur at 1, 2 and 4 that are the first 3 terms of this sequence.

Mathematica

With[{s = Array[Times @@ FactorInteger[#, GaussianIntegers -> True][[All, -1]] &, 10^5]}, Map[FirstPosition[s, #][[1]] &, Union@FoldList[Max, s]]] (* after Michael De Vlieger at A005934 *)

Crossrefs

Cf. A005934, A279254, A335851, A335852.

Sequence in context: A318588 A008881 A208743 * A247213 A302934 A069050

Adjacent sequences: A335850 A335851 A335852 * A335854 A335855 A335856

Keyword

nonn

Author

Amiram Eldar, Jun 26 2020

Status

approved