A332317 -id:A332317 - cp's OEIS frontend

A332477 Numbers k that are unitary harmonic in Gaussian integers: k * A332476(k) is divisible by A332472(k) + i*A332473(k) (where i is the imaginary unit).

1, 5, 12, 50, 60, 84, 300, 420, 450, 756, 900, 1950, 3780, 7800, 9900, 33150, 49140, 54600, 100800, 132600, 265200, 491400, 928200, 1856400, 8353800, 8884200, 16707600, 52211250, 65995776, 78566400, 182739375, 183783600, 208845000, 280348992, 293046000, 329978880

Offset: 1

Amiram Eldar, Feb 13 2020

nonn

Analogous to unitary harmonic numbers (A006086), with the number and sum of unitary divisors functions generalized for Gaussian integers (A332476, A332472 + i * A332473) instead of the number and sum of unitary divisors functions (A034444, A034448).

			5 is a term since 5 * A332476(5)/(A332472(5) + i*A332473(5)) = 5 * 4/(4 + 8*i) = 1 - 2*i is a Gaussian integer.

Amiram Eldar, Table of n, a(n) for n = 1..75

Cf. A034444, A034448, A006086, A332317, A332472, A332473, A332476.

sigma[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; tau[p_, e_] := If[Abs[p] == 1, 1, 2]; unitaryHarmonicQ[n_] := Divisible[n * Times @@ tau @@@ (f = FactorInteger[n, GaussianIntegers -> True]), Times @@ sigma @@@ f]; Select[Range[10^5], unitaryHarmonicQ]

cp's OEIS Frontend

A332477 Numbers k that are unitary harmonic in Gaussian integers: k * A332476(k) is divisible by A332472(k) + i*A332473(k) (where i is the imaginary unit).

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