A335853 - OEIS

%I #12 Jun 30 2020 05:33:05

%S 1,2,4,8,16,32,64,100,200,400,500,800,1000,2000,4000,5000,8000,10000,

%T 18000,20000,27000,36000,40000,50000,54000,80000,90000,108000,135000,

%U 180000,216000,270000,450000,540000,810000,1080000,1350000,1620000,2160000,2700000

%N Numbers that are highly powerful in Gaussian integers.

%C 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.

%C 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).

%H Amiram Eldar, <a href="/A335853/b335853.txt">Table of n, a(n) for n = 1..81</a>

%H Amiram Eldar, <a href="/A335853/a335853.txt">Table of n, a(n), A335852(a(n)) for n = 1..81</a>

%e 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.

%t 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 *)

%Y Cf. A005934, A279254, A335851, A335852.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jun 26 2020