A281993 - OEIS

%I #24 Feb 11 2020 04:22:24

%S 10,44,184,752,12224,49024,12580864,206158168064,

%T 885443715520878608384,226673591177468092350464,

%U 232113757366000005450563584,3894222643901120685369075227951104,1020847100762815390371677078221595082752,17126972312471518572699356075530215722269540352

%N Integers m such that sigma(m) + sigma(2*m) = 6*m.

%C This is the case h = 2 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^A002235(n+1) * A007505(n+1). - _Daniel Suteu_, Feb 08 2017 [See Harborth link for a proof.]

%e 10 is a term since sigma(10) + sigma(20) = 60, that is 6*10.

%t Select[Range[10^7], DivisorSigma[1, #] + DivisorSigma[1, 2 #] == 6 # &] (* _Michael De Vlieger_, Feb 04 2017 *)

%o (PARI) isok(n, h=2) = sigma(n) + sigma(h*n) == 2*n*(h+1);

%Y Cf. A000203, A097215.

%K nonn

%O 1,1

%A _Michel Marcus_, Feb 04 2017

%E More terms from _Jinyuan Wang_, Feb 11 2020