

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



1, 5, 130, 390, 585, 3250, 31980, 133250, 223860, 799500, 7195500, 13591500, 122323500, 258238500, 394153500, 405346500, 910630500, 1345558500, 2025133500, 8195674500
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



