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A005276 Betrothed (or quasi-amicable) numbers.
(Formerly M5291)
11
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)
OFFSET

1,1

COMMENTS

Members of a pair (m,n) such that sigma(m)=sigma(n)=m+n+1, where sigma=A000203. [From 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. [From Juri-Stepan Gerasimov, Sep 11 2009]

Also numbers that are terms of cycles when iterating Chowla's function A048050. - Reinhard Zumkeller, Feb 09 2013

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B5.

P. Hagis and G. Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611.

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

LINKS

T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from T. D. Noe)

Eric Weisstein's World of Mathematics, Quasiamicable Pair.

FORMULA

A005276 = A003502 union A003503. [From M. F. Hasler, Nov 04 2008]

MATHEMATICA

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 *)

PROG

Contribution from M. F. Hasler, Nov 04 2008: (Start)

(PARI) isA005276(n) = { local(s=sigma(n)); s>n+1 & sigma(s-n-1)==s }

for( n=1, 10^6, isA005276(n) & print1(n", ")) (End)

(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

CROSSREFS

Cf. A003502, A003503.

Cf. A048050, subsequence of A057533.

Sequence in context: A165039 A211721 A057533 * A143722 A110229 A108608

Adjacent sequences:  A005273 A005274 A005275 * A005277 A005278 A005279

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended by T. D. Noe, Dec 29 2011

STATUS

approved

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Last modified July 30 09:31 EDT 2014. Contains 245062 sequences.