Search: id:A006036
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%I A006036 M4133
%S A006036 6,20,28,88,104,272,304,350,368,464,490,496,550,572,650,748,770,910,
%T A006036 945,1184,1190,1312,1330,1376,1430,1504,1575,1610,1696,1870,1888,
%U A006036 1952,2002,2030,2090,2170,2205,2210,2470,2530,2584,2590,2870,2990,3010,
               3128,3190,3230,3290,3410,3465,3496,3710,3770,3944,4070,4095,4130,
               4216,4270,4288,4408,4510,4544,4672,4690,4712,4730,4970
%N A006036 Primitive pseudoperfect numbers.
%C A006036 A primitive pseudoperfect number is a pseudoperfect number that is not 
               a multiple of any other pseudoperfect number.
%C A006036 The odd entries so far are identical to the odd primitive abundant A006038. 
               - Walter A. Kehowski (wkehowski(AT)cox.net), Aug 12 2005
%D A006036 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006036 R. K. Guy, Unsolved Problems in Number Theory, B2.
%H A006036 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimitiveSemiperfectNumber.html">Link to a section of The World of 
               Mathematics.</a>
%p A006036 with(numtheory): with(combinat): issemiperfect := proc(n) local b, S;
%p A006036 b:=false; S:=subsets(divisors(n) minus {n}); while not S[finished] do 
               if
%p A006036 convert(S[nextvalue](),`+`)=n then b:=true; break fi od; return b end:
%p A006036 L:=remove(proc(z) isprime(z) end,[$1..5000]): PP:=[]: for zz from 1 to 
               1 do
%p A006036 for n in L do if issemiperfect(n) then PP:=[op(PP),n] fi od od;
%p A006036 sr := proc(l::list) local x, R, S, P, L; S:=sort(l); R:=[]; P:=S;
%p A006036 for x in S do
%p A006036 if not(x in R) then
%p A006036 L:=selectremove(proc(z) z>x and z mod x = 0 end, P);
%p A006036 R:=[op(R),op(L[1])]; P:=L[2];
%p A006036 fi; od; return P; end:
%p A006036 PPP:=sr(PP); # primitive pseudoperfect numbers less than 5000 (Walter 
               A. Kehowski)
%Y A006036 Cf. A005835.
%Y A006036 Sequence in context: A119425 A006039 A064771 this_sequence A140738 A031005 
               A106528
%Y A006036 Adjacent sequences: A006033 A006034 A006035 this_sequence A006037 A006038 
               A006039
%K A006036 nonn,nice
%O A006036 1,1
%A A006036 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A006036 More terms from Walter A. Kehowski (wkehowski(AT)cox.net), Aug 12 2005

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