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 A005276 Betrothed (or quasi-amicable) 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 (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. - 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 From Amiram Eldar, Mar 09 2024: (Start) 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 "quasi-amicable 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. 91-92. 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 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) Walter E. Beck and Rudolph M. Wajar, More reduced amicable pairs, Fibonacci Quarterly, Vol. 15, No. 4 (1977), pp. 331-332. Walter E. Beck and Rudolph M. Wajar, Reduced and Augmented Amicable Pairs to 10^8, Fibonacci Quarterly, Vol. 31, No. 4 (1993), pp. 295-298. Peter Hagis and Graham Lord, Quasi-amicable numbers, Math. Comp. 31 (1977), 608-611. M. Lal and A. Forbes, A note on Chowla's function, Math. Comp., Vol. 25, No. 116 (1971), pp. 923-925. A. Makowski, On Some Equations Involving Functions phi(n) and sigma(n), The American Mathematical Monthly, Vol. 67, No. 7 (1960), pp. 668-670. Abdur Rahman Nasir, On a certain arithmetic function, Bull. Calcutta Math. Soc., Vol. 38 (1946), p. 140. 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.. Wikipedia, Betrothed numbers. FORMULA Equals 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, A048050, A328370. 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

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Last modified August 7 01:21 EDT 2024. Contains 375002 sequences. (Running on oeis4.)