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

Author

Amiram Eldar, Jun 26 2020

Keywords

• nonn

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).

Examples

			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.
		

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

Crossrefs

Cf. A005934, A279254, A335851, A335852.

Programs

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 *)