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Integers m such that sigma(m) + sigma(8*m) = 18*m.
2

%I #8 Feb 24 2020 04:24:32

%S 34,568,147328,603971584,9663643648,39582416502784,

%T 696341272098017608537735168,765635325572111542783369494684623699968,

%U 3615610599582728119969414707766982030374842621310535527825408,3791242500068058721125048996612134914443116117566314438843154038784

%N Integers m such that sigma(m) + sigma(8*m) = 18*m.

%C This is the case h = 8 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^A002236(n) * A050524(n).

%e 34 is a term since sigma(34) + sigma(8*34) = 612, that is 18*34.

%o (PARI) isok(m) = sigma(m) + sigma(8*m) == 18*m;

%Y Cf. A000203, A000396, A002236, A050524, A136539, A281993, A330413.

%K nonn

%O 1,1

%A _Jinyuan Wang_, Feb 12 2020