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Integers m such that sigma(m) + sigma(16*m) = 34*m.
2

%I #7 Feb 24 2020 04:25:00

%S 268,4336,69568,73014378496,18691696623616,80280230208715249156096,

%T 5516815412193254337299253840314368,

%U 22596875928343569838211798520159010816,106710729501573572985208420194451100911225778218295042768896,7689318425915528602346510723233181380859942271270135051778769275060995751936

%N Integers m such that sigma(m) + sigma(16*m) = 34*m.

%C This is the case h = 16 of the h-perfect numbers as defined in the Harborth link.

%H Heiko Harborth, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from57to62.pdf">On h-perfect numbers</a>, Annales Mathematicae et Informaticae, 41 (2013) pp. 57-62.

%F a(n) = 2^A001774(n) * (17*2^A001774(n) - 1).

%e 268 is a term since sigma(268) + sigma(16*268) = 9112, that is 34*268.

%o (PARI) isok(m) = sigma(m) + sigma(16*m) == 34*m;

%Y Cf. A000203, A000396, A001774, A136539, A281993, A330412.

%K nonn

%O 1,1

%A _Jinyuan Wang_, Feb 12 2020