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A006036 Primitive pseudoperfect numbers.
(Formerly M4133)
4
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)

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 * A140738 A226363 A031005

Adjacent sequences:  A006033 A006034 A006035 * A006037 A006038 A006039

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, R. K. Guy

EXTENSIONS

More terms from Walter Kehowski, Aug 12 2005

STATUS

approved

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Last modified April 21 02:07 EDT 2014. Contains 240824 sequences.