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 A006036 Primitive pseudoperfect numbers. (Formerly M4133) 7

%I M4133

%S 6,20,28,88,104,272,304,350,368,464,490,496,550,572,650,748,770,910,

%T 945,1184,1190,1312,1330,1376,1430,1504,1575,1610,1696,1870,1888,1952,

%U 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 Primitive pseudoperfect numbers.

%C A primitive pseudoperfect number is a pseudoperfect number that is not a multiple of any other pseudoperfect number.

%C The odd entries so far are identical to the odd primitive abundant A006038. - _Walter Kehowski_, Aug 12 2005

%D R. K. Guy, Unsolved Problems in Number Theory, B2.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Donovan Johnson, <a href="/A006036/b006036.txt">Table of n, a(n) for n = 1..10000</a>

%H R. K. Guy, <a href="/A001599/a001599_1.pdf">Letter to N. J. A. Sloane with attachment, Jun. 1991</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitivePseudoperfectNumber.html">Primitive Pseudoperfect Number</a>

%p with(numtheory): with(combinat): issemiperfect := proc(n) local b, S;

%p b:=false; S:=subsets(divisors(n) minus {n}); while not S[finished] do if

%p convert(S[nextvalue](),`+`)=n then b:=true; break fi od; return b end:

%p L:=remove(proc(z) isprime(z) end,[\$1..5000]): PP:=[]: for zz from 1 to 1 do

%p for n in L do if issemiperfect(n) then PP:=[op(PP),n] fi od od;

%p sr := proc(l::list) local x, R, S, P, L; S:=sort(l); R:=[]; P:=S;

%p for x in S do

%p if not(x in R) then

%p L:=selectremove(proc(z) z>x and z mod x = 0 end, P);

%p R:=[op(R),op(L[1])]; P:=L[2];

%p fi; od; return P; end:

%p PPP:=sr(PP); # primitive pseudoperfect numbers less than 5000 # _Walter Kehowski_, Aug 12 2005

%t (* 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 *)

%o a006036 n = a006036_list !! (n-1)

%o a006036_list = filter (all (== 0) . map a210455 . a027751_row) a005835_list

%o -- _Reinhard Zumkeller_, Jan 21 2013

%Y Cf. A005835.

%Y Cf. A210455, A027751.

%K nonn,nice

%O 1,1

%A _N. J. A. Sloane_, _R. K. Guy_

%E More terms from _Walter Kehowski_, Aug 12 2005

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Last modified February 22 11:50 EST 2020. Contains 332135 sequences. (Running on oeis4.)