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A006036
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Primitive pseudoperfect numbers.
(Formerly M4133)
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4
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6, 20, 28, 88, 104, 272, 304, 350, 368, 464, 490, 496, 550, 572, 650, 748, 770, 910, 945, 1184, 1190, 1312, 1330, 1376, 1430, 1504, 1575, 1610, 1696, 1870, 1888, 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
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OFFSET
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1,1
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COMMENTS
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A primitive pseudoperfect number is a pseudoperfect number that is not a multiple of any other pseudoperfect number.
The odd entries so far are identical to the odd primitive abundant A006038. - Walter Kehowski, Aug 12 2005
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B2.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Donovan Johnson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Pseudoperfect Number
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MAPLE
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with(numtheory): 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:
L:=remove(proc(z) isprime(z) end, [$1..5000]): PP:=[]: for zz from 1 to 1 do
for n in L do if issemiperfect(n) then PP:=[op(PP), n] fi od od;
sr := proc(l::list) local x, R, S, P, L; S:=sort(l); R:=[]; P:=S;
for x in S do
if not(x in R) then
L:=selectremove(proc(z) z>x and z mod x = 0 end, P);
R:=[op(R), op(L[1])]; P:=L[2];
fi; od; return P; end:
PPP:=sr(PP); # primitive pseudoperfect numbers less than 5000 (Walter A. Kehowski)
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MATHEMATICA
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(* First run one of the programs for A005835 *) A006036 = A005835; curr = 1; max = A005835[[-1]]; While[curr < Length[A006036], currMult = A006036[[curr]]; A006036 = Complement[A006036, Range[2currMult, Ceiling[max/currMult] currMult, currMult]]; curr++]; A006036 (* Alonso del Arte, Sep 08 2012 *)
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PROG
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(Haskell)
a006036 n = a006036_list !! (n-1)
a006036_list = filter (all (== 0) . map a210455 . a027751_row) a005835_list
-- Reinhard Zumkeller, Jan 21 2013
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CROSSREFS
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Cf. A005835.
Cf. A210455, A027751.
Sequence in context: A006039 A180332 A064771 * A140738 A031005 A106528
Adjacent sequences: A006033 A006034 A006035 * A006037 A006038 A006039
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane, R. K. Guy
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EXTENSIONS
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More terms from Walter Kehowski, Aug 12 2005
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STATUS
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approved
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