A332478 Number that are unitary norm-multiply-perfect numbers in Gaussian integers.

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.

Links

Table of n, a(n) for n=1..7.

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

Cf. A002827, A327158, A332318, A332319, A332474.

Sequence in context: A255534 A262422 A248336 * A144814 A378488 A241174

Adjacent sequences: A332475 A332476 A332477 * A332479 A332480 A332481

Keyword

nonn,more

Author

Amiram Eldar, Feb 13 2020

Status

approved