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

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

Offset

1,1

Comments

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

References

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).

Links

Giovanni Resta, Table of n, a(n) for n = 1..7819 (terms < 10^13, terms 1..100 from T. D. Noe, 101..1000 from Donovan Johnson)

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.

Formula

A005276 = A003502 union A003503. - 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

(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

Crossrefs

Cf. A003502, A003503.

Cf. A048050, subsequence of A057533.

Sequence in context: A165039 A211721 A057533 * A328370 A143722 A261709

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