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A332478
Number that are unitary norm-multiply-perfect numbers in Gaussian integers.
0
1, 10, 12, 20160, 15713280, 137592000, 44289146880
OFFSET
1,2
COMMENTS
Numbers k such that their norm of sum of unitary divisors in Gaussian integers, A332474(k), is divisible by their norm, k^2.
The corresponding ratios A332474(a(n))/(a(n)^2) are 1, 4, 1, 5, 5, 2, 5.
EXAMPLE
10 is a term since its sum of unitary divisors in Gaussian integers is -12 + 16*i, whose norm (-12)^2 + 16^2 = 400 is divisible by 10^2 = 100.
MATHEMATICA
f[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; Select[Range[21000], Divisible[Abs[ Times @@ f @@@ FactorInteger[#, GaussianIntegers -> True]]^2, #^2] &]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Feb 13 2020
STATUS
approved