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A109761 Rare pseudoperfect (or semiperfect) numbers, that is, pseudoperfect numbers k such that k == 2 or 10 (mod 12).

%I A109761 #20 Feb 10 2021 01:10:37
%S A109761 350,490,550,650,770,910,1190,1330,1430,1610,1750,1870,2002,2030,2090,
%T A109761 2170,2210,2450,2470,2530,2590,2750,2870,2990,3010,3190,3230,3250,
%U A109761 3290,3410,3430,3710,3770,3850,4070,4130,4270,4510,4550,4690,4730,4970
%N A109761 Rare pseudoperfect (or semiperfect) numbers, that is, pseudoperfect numbers k such that k == 2 or 10 (mod 12).
%C A109761 There are 1232 pseudoperfect numbers less than or equal to 5000 but only 42 rare ones.
%H A109761 Amiram Eldar, <a href="/A109761/b109761.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..250 from Reinhard Zumkeller)
%p A109761 with(combinat); issemiperfect := proc(n) local b, S; b:=false; S:=subsets(divisors(n) minus {n}); while not S[finished] do if convert(S[nextvalue](),`+`)=n then b:=true; break fi od; return b end: S:=remove(proc(z) type(z,odd) end,[$1..5000]): SP:=select(proc(z) issemiperfect(z) end, S): RSP:=select(proc(z) z mod 12 = 2 or z mod 12 = 10 end, SP);
%o A109761 (Haskell)
%o A109761 a109761 n = a109761_list !! (n-1)
%o A109761 a109761_list = filter ((== 1) . a210455) a091999_list
%o A109761 -- _Reinhard Zumkeller_, Jan 21 2013
%Y A109761 Cf. A005835.
%Y A109761 Cf. A210455; intersection of A005835 and A091999.
%K A109761 nonn
%O A109761 1,1
%A A109761 _Walter Kehowski_, Aug 12 2005