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A335853
Numbers that are highly powerful in Gaussian integers.
1
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).
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 26 2020
STATUS
approved