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Search: id:A083209
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| A083209 |
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Numbers with exactly one subset of their sets of divisors such that the complement has the same sum. |
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+0
4
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| 6, 12, 20, 28, 56, 70, 88, 104, 176, 208, 272, 304, 368, 464, 496, 550, 650, 736, 836, 928, 992, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 2752, 3008, 3230, 3392, 3770, 3776, 3904, 4030, 4288, 4510, 4544, 4672, 5056, 5170, 5312, 5696, 5830, 6208, 6464
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The weird numbers A006037 are not a subset of this sequence. The first missing weird number is A006037(8) = 10430. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009]
A083206(a(n))=1; perfect numbers (A000396) are a subset; problem: are weird numbers (A006037) a subset?
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LINKS
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Alois P. Heinz, Table of n, a(n) for n=1..100
Eric Weisstein's World of Mathematics, Perfect Number.
Eric Weisstein's World of Mathematics, Weird Number.
Reinhard Zumkeller, Illustration of initial terms
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EXAMPLE
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n=20: 2+4+5+10=1+20, 20 is a term (A083206(20)=1).
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MAPLE
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with (numtheory): b:= proc(n, l) option remember; local m, ll, i; m:= nops(l); if n<0 then 0 elif n=0 then 1 elif m=0 or add (i, i=l)<n then 0 else ll:= subsop (m=NULL, l); b(n, ll) +b(n-l[m], ll) fi end: a:= proc(n) option remember; local i, k, l, m, r; for k from `if`(n=1, 1, a(n-1)+1) do l:= sort ([divisors (k)[]]); m:= iquo (add (i, i=l), 2, 'r'); if r=0 and b(m, l)=2 then break fi od; k end: seq (a(n), n=1..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009]
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CROSSREFS
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Cf. A005101, A005835, A064771.
Sequence in context: A094371 A079760 A109895 this_sequence A080714 A116368 A007622
Adjacent sequences: A083206 A083207 A083208 this_sequence A083210 A083211 A083212
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KEYWORD
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nonn,new
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2003
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 29 2009
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