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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

LINKS

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

EXAMPLE

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.

MATHEMATICA

sigma[p_, e_] := If[Abs[p] == 1, 1, (p^e + 1)]; tau[p_, e_] := If[Abs[p] == 1, 1, 2]; unitaryHarmoincQ[n_] := Divisible[n * Times @@ tau @@@ (f = FactorInteger[n, GaussianIntegers -> True]), Times @@ sigma @@@ f]; Select[Range[10^6], unitaryHarmoincQ]

CROSSREFS

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

Sequence in context: A211951 A009425 A009416 * A240389 A135769 A074024

Adjacent sequences:  A332474 A332475 A332476 * A332478 A332479 A332480

KEYWORD

nonn

AUTHOR

Amiram Eldar, Feb 13 2020

STATUS

approved

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Last modified September 25 00:00 EDT 2020. Contains 337329 sequences. (Running on oeis4.)