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%I #8 May 30 2020 04:08:18
%S 5829840,3414097920,39339578248
%N Numbers k such that ab(k) + ab(k+1) + ab(k+2) = 0, where ab(k) is the abundance of k (A033880).
%C Equivalently, s(k) + s(k+1) + s(k+2) = k + (k+1) + (k+2), where s(k) is the sum of proper divisors of k (A001065).
%C a(4) > 10^11, if it exists.
%C a(4) > 10^13, if it exists. - _Giovanni Resta_, May 30 2020
%e 5829840 is a term since ab(5829840) + ab(5829841) + ab(5829842) = 8428320 - 5513402 - 2914918 = 0.
%t s[n_] := DivisorSigma[1, n] - n; Select[Range[6 * 10^6], s[#] + s[# + 1] + s[# + 2] == 3*# + 3 &]
%Y Cf. A000203, A001065, A033880, A335254.
%K nonn,hard,bref,more
%O 1,1
%A _Amiram Eldar_, May 28 2020
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