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%I #30 Jan 24 2023 15:30:34
%S 180,12000,30996,47940,66780,102816,128040,234300,494088,712272,
%T 1133088,1408212,1623072,1692768,1896336,1925196,2024760,2388720,
%U 2529090,2836008,3423120,3724320,3822360,4628760,4750920,7219608,7359912,7603488,7749060
%N Numbers k such that sigma(k) = 3*sigma(k+1).
%H Donovan Johnson, <a href="/A217791/b217791.txt">Table of n, a(n) for n = 1..500</a>
%e 47940 is in the sequence because sigma(47940)=145152, sigma(47941)=48384, and 145152=3*48384.
%e 7749060 is in the sequence because sigma(7749060)=24192000, sigma(7749061)=8064000, and 24192000=3*8064000.
%p A217791:=proc(q) local n;
%p for n from 1 to q do if sigma(n)=3*sigma(n+1) then print(n); fi; od; end:
%p A217791(10^10);
%t Position[Partition[DivisorSigma[1,Range[78*10^5]],2,1],_?(#[[1]] == 3#[[2]]&), {1},Heads->False]//Flatten (* _Harvey P. Dale_, Oct 17 2016 *)
%o (Magma) [n: n in [1..10^7] | SumOfDivisors(n) eq 3*SumOfDivisors(n+1)]; // _Bruno Berselli_, Mar 25 2013
%Y Cf. A000203, A002961, A058073, A067081, A077087, A163193, A272027 (3*sigma(n)).
%K nonn
%O 1,1
%A _Paolo P. Lava_, Mar 25 2013
%E More terms from _Bruno Berselli_, Mar 25 2013
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