

A005276


Betrothed (or quasiamicable) numbers.
(Formerly M5291)


15



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
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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.  JuriStepan Gerasimov, Sep 11 2009
The first pair, (48, 75), was found by Nasir (1946).
Lehmer (1948) in a review of Nasir's paper, noted that "the pair (48, 75) behave like amicable numbers".
Makowski (1960) found the next 2 pairs, and called them "pairs of almost amicable numbers".
The next 6 pairs were found by independently by Garcia (1968), who named them "números casi amigos" and Lal and Forbes (1971), who named them "reduced amicable pairs".
Beck and Wajar (1971) found 6 more pairs, but missed the 15th and 16th pairs, (526575, 544784) and (573560, 817479).
Hagis and Lord (1977) found the first 46 pairs. They called them "quasiamicable numbers", after Garcia (1968).
Beck and Wajar (1993) found the next 33 pairs.
According to Guy (2004; 1st ed., 1981), the name "betrothed numbers" was proposed by Rufus Isaacs. (End)


REFERENCES

Mariano Garcia, Números Casi Amigos y Casi Sociables, Revista Annal, año 1, October 1968, Asociación Puertorriqueña de Maestros de Matemáticas.
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B5, pp. 9192.
D. H. Lehmer, Math. Rev., Vol. 8 (1948), p. 445.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS



FORMULA



MATHEMATICA

bnoQ[n_]:=Module[{dsn=DivisorSigma[1, n], m, dsm}, m=dsnn1; 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(sn1)==s }
for( n=1, 10^6, isA005276(n) & print1(n", ")) \\ M. F. Hasler, Nov 04 2008
(Haskell)
a005276 n = a005276_list !! (n1)
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


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



EXTENSIONS



STATUS

approved



