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A002025
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Smaller of amicable pair.
(Formerly M5414 N2352)
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20
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220, 1184, 2620, 5020, 6232, 10744, 12285, 17296, 63020, 66928, 67095, 69615, 79750, 100485, 122265, 122368, 141664, 142310, 171856, 176272, 185368, 196724, 280540, 308620, 319550, 356408, 437456, 469028, 503056, 522405, 600392, 609928
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sometimes called friendly numbers, but this usage is deprecated.
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REFERENCES
| J. Alanen, O. Ore and J. Stemple, Systematic computations on amicable numbers, Math. Comp., 21 (1967), 242-245.
W. Borho and H. Hoffmann, Breeding Amicable Numbers in Abundance, Math. Comp., 46 (1986), 281-293.
Mariano Garcia, Jan Munch Pedersen and Herman te Riele, Amicable pairs - a survey, pp. 179-196 in: Alf van der Poorten and Andres Stein (eds.), High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS, Providence RI, 2004.
E. J. Lee, Amicable Numbers and the Bilinear Diophantine Equation, Math. Comp., 22 (1968), 181-187.
E. J. Lee and J. S. Madachy, The History and Discovery of Amicable Numbers, J. Recr. Math. 5 (1972) pp. 77-93, 153-173, 231-249. Errata in vol. 6, pp. 53, 164 and 229.
H. J. J. te Riele, Four large amicable pairs, Math. Comp., 28 (1974), 309-312.
H. J. J. te Riele, Computation of all the amicable pairs below 10^10, Math. Comp., 47 (1986), 361-368 and Supplement pp. S9-S40.
H. J. J. te Riele et al., Table of Amicable Pairs between 10^10 and 10^52, Note NM-N8603, Department of Numerical Mathematics, Centre for Mathematics and Computer Science, Amsterdam, 1986.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..39374 (terms < 10^14 from Pedersen's tables)
J. Bell, A translation of Leonhard Euler's...
L. Euler, De numeris amicabilibus, Opuscula varii argumetii, pages 23-107, 1750. Reprinted in Opera mathematica: Series prima. Volumen II, Leonhardi Euleri commentationes arithmeticae. Sub ausp. soc. scient. nat. Helv., Teubner, Leipzig, Series I, Vol. 1915, pp. 86-162.
M. Garcia, A Million New Amicable Pairs, J. Integer Seqs., Vol. 4 (2001), #01.2.6.
S. S. Gupta, Amicable Numbers
Hisanori Mishima, First 236 amicable pairs
D. Moews, Perfect, amicable and sociable numbers
J. O. M. Pedersen, Known Amicable Pairs
J. O. M. Pedersen, Tables of Aliquot Cycles
T. Trotter, Jr., Amicable Numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
| lim = 10^6; amicableQ[n_] := With[{s = DivisorSigma[1, n] - n}, n == DivisorSigma[1, s] - s && n < s]; Select[ Range[lim], amicableQ] (* From Jean-François Alcover, Sep 20 2011 *)
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PROG
| Contribution from Michael B. Porter (michael_b_porter(AT)yahoo.com), Apr 11 2010: (Start)
(PARI) aliquot(n)=sigma(n)-n
isA002025(n)={local(a); a=aliquot(n); a>n && aliquot(a)==n} (End)
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CROSSREFS
| Cf. A002046, A063990.
Cf. A066873.
Sequence in context: A184543 A135807 A102073 * A180219 A027797 A055663
Adjacent sequences: A002022 A002023 A002024 * A002026 A002027 A002028
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Oct 24 2000
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