A332317 - OEIS

%I #6 Feb 09 2020 20:11:31

%S 1,5,130,390,585,3250,31980,133250,223860,799500,7195500,13591500,

%T 122323500,258238500,394153500,405346500,910630500,1345558500,

%U 2025133500,8195674500

%N 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).

%C 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).

%C No more terms below 10^10.

%e 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.

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

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

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Feb 09 2020