A332317 Numbers k that are harmonic in Gaussian integers: k * A062327(k) is divisible by A103228(k) + i*A103229(k) (where i is the imaginary unit).

1, 5, 130, 390, 585, 3250, 31980, 133250, 223860, 799500, 7195500, 13591500, 122323500, 258238500, 394153500, 405346500, 910630500, 1345558500, 2025133500, 8195674500

Offset

1,2

Comments

Analogous to harmonic numbers (A001599), with the number and sum of divisors functions generalized for Gaussian integers (A062327, A103228, A103229) instead of the number and sum of divisors functions (A000005, A000203).

No more terms below 10^10.

Links

Table of n, a(n) for n=1..20.

Example

5 is a term since 5 * A062327(5)/(A103228(5) + i*A103229(5)) = 5 * 4 /(4 + 8*i) = 1 - 2*i is a Gaussian integer.

Mathematica

Select[Range[10^4], Divisible[# * DivisorSigma[0, #, GaussianIntegers -> True], DivisorSigma[1, #, GaussianIntegers -> True]] &]

Crossrefs

Cf. A000005, A000203, A001599, A062327, A103228, A103229, A103230.

Sequence in context: A012083 A012226 A281818 * A069078 A003732 A203476

Adjacent sequences: A332314 A332315 A332316 * A332318 A332319 A332320

Keyword

nonn,more

Author

Amiram Eldar, Feb 09 2020

Status

approved