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A318272 a(n) is the least k such that A049417(A049417(k)) = n*k, where A049417 is the infinitary sigma function, or 0 if no such k exists.

%I A318272 #23 Sep 08 2018 18:55:38
%S A318272 1,2,8,15,24,60,1321920,17850,285600,763776
%N A318272 a(n) is the least k such that A049417(A049417(k)) = n*k, where A049417 is the infinitary sigma function, or 0 if no such k exists.
%C A318272 It is also known that a(12) = 71400.
%C A318272 Then for higher indices n, we have:
%C A318272   a(11) <= 414230544000;
%C A318272   a(13) <= 2667897127526400;
%C A318272   a(14) <= 446464417259520;
%C A318272   a(15) <= 23613006957281280;
%C A318272   a(16) <= 22227004800;
%C A318272   a(17) <= 3134896756992000;
%C A318272   a(18) <= 15414516736819200;
%C A318272   a(20) <= 53129265653882880.
%C A318272 a(16) = 8420630400. - _Giovanni Resta_, Aug 25 2018
%H A318272 Tomohiro Yamada, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_47_from211to218.pdf">Infinitary superperfect numbers</a>, Annales Mathematicae et Informaticae, 47 (2017) pp. 211-218. See Table 1.
%Y A318272 Cf. A049417, A318182.
%Y A318272 Cf. A272930 (analog for sigma), A318242 (analog for bi-unitary sigma).
%K A318272 nonn,more
%O A318272 1,2
%A A318272 _Michel Marcus_, Aug 23 2018