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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
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.
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]] &]
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Feb 09 2020
STATUS
approved