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Numbers k such that k and k + 1 have the same norm of the sum of divisors in Gaussian integers.
1

%I #4 Feb 09 2020 20:11:20

%S 30514,36777,43978,3474262,5745125,10628554,16567494,40831527,

%T 58008301,111798477,142981839,288834504,392413941,580867202,650141557,

%U 944224497,967593411,1874210882,6306287377,6442064745,7377567197,8121464245

%N Numbers k such that k and k + 1 have the same norm of the sum of divisors in Gaussian integers.

%C The first term, 30514, is also a number k such that k and k + 1 have the sum divisors in Gaussian integers: -54720 + 48960*i (where i is the imaginary unit). What is the next term with this property?

%C No more terms below 1.5*10^10.

%e 30514 is a term since A103230(30514) = A103230(30515) = 5391360000.

%t csigma[n_] :=(Abs @ DivisorSigma[1, n, GaussianIntegers -> True])^2; seq = {}; n1 = csigma[1]; Do[n2 = csigma[n]; If[n1 == n2, AppendTo[seq, n - 1]]; n1 = n2, {n, 2, 5*10^5}]; seq

%Y Cf. A002961, A064125, A103228, A103229, A103230, A293183, A306985.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Feb 09 2020