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 A006036 Primitive pseudoperfect numbers. (Formerly M4133) 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES 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). LINKS Donovan Johnson, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Primitive Pseudoperfect Number MAPLE 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_, Aug 12 2005 MATHEMATICA (* 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 *) PROG (Haskell) a006036 n = a006036_list !! (n-1) a006036_list = filter (all (== 0) . map a210455 . a027751_row) a005835_list -- Reinhard Zumkeller, Jan 21 2013 CROSSREFS Cf. A005835. Cf. A210455, A027751. Sequence in context: A006039 A180332 A064771 * A242341 A140738 A226363 Adjacent sequences:  A006033 A006034 A006035 * A006037 A006038 A006039 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Walter Kehowski, Aug 12 2005 STATUS approved

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Last modified November 17 14:58 EST 2017. Contains 294834 sequences.