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A005276
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Betrothed (or quasi-amicable) numbers.
(Formerly M5291)
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13
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48, 75, 140, 195, 1050, 1575, 1648, 1925, 2024, 2295, 5775, 6128, 8892, 9504, 16587, 20735, 62744, 75495, 186615, 196664, 199760, 206504, 219975, 266000, 309135, 312620, 507759, 526575, 544784, 549219, 573560, 587460, 817479, 1000824, 1057595, 1081184
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Members of a pair (m,n) such that sigma(m)=sigma(n)=m+n+1, where sigma=A000203. [M. F. Hasler, Nov 04 2008]
Also members of a pair (m,k) such that m = sum of nontrivial divisors of k and k = sum of nontrivial divisors of m. [Juri-Stepan Gerasimov, Sep 11 2009]
Also numbers that are terms of cycles when iterating Chowla's function A048050. - Reinhard Zumkeller, Feb 09 2013
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B5.
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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T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from T. D. Noe)
P. Hagis and G. Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611.
Paul Pollack, Quasi-Amicable Numbers are Rare, Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.2.
Eric Weisstein's World of Mathematics, Quasiamicable Pair.
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FORMULA
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A005276 = A003502 union A003503. [M. F. Hasler, Nov 04 2008]
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MATHEMATICA
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bnoQ[n_]:=Module[{dsn=DivisorSigma[1, n], m, dsm}, m=dsn-n-1; dsm=DivisorSigma[ 1, m]; dsm==dsn==n+m+1]; Select[Range[2, 1100000], bnoQ] (* Harvey P. Dale, May 12 2012 *)
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PROG
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(PARI) isA005276(n) = { local(s=sigma(n)); s>n+1 & sigma(s-n-1)==s }
for( n=1, 10^6, isA005276(n) & print1(n", ")) \\ M. F. Hasler, Nov 04 2008
(Haskell)
a005276 n = a005276_list !! (n-1)
a005276_list = filter p [1..] where
p z = p' z [0, z] where
p' x ts = if y `notElem` ts then p' y (y:ts) else y == z
where y = a048050 x
-- Reinhard Zumkeller, Feb 09 2013
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CROSSREFS
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Cf. A003502, A003503.
Cf. A048050, subsequence of A057533.
Sequence in context: A165039 A211721 A057533 * A143722 A261709 A261704
Adjacent sequences: A005273 A005274 A005275 * A005277 A005278 A005279
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Extended by T. D. Noe, Dec 29 2011
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STATUS
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approved
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