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A002046 Larger of amicable pair.
(Formerly M5435 N2363)
75
284, 1210, 2924, 5564, 6368, 10856, 14595, 18416, 76084, 66992, 71145, 87633, 88730, 124155, 139815, 123152, 153176, 168730, 176336, 180848, 203432, 202444, 365084, 389924, 430402, 399592, 455344, 486178, 514736, 525915, 669688, 686072 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The elements 76084, 123152, etc. are intentionally out of numerical order so that a(n) and A002025(n) form amicable pairs. - Michael B. Porter, Apr 17 2010
All terms are deficient (A005100). - Michel Marcus, Mar 10 2013
For the related amicable pairs see A259180. - Omar E. Pol, Jul 15 2015
REFERENCES
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).
For additional references see A002025.
LINKS
T. D. Noe and Sergei Chernykh, Table of n, a(n) for n = 1..415523 [All terms such that the smaller number A002025(n) is < 10^17. Terms 39375 through 415523 were computed by Sergei Chernykh]
J. Bell, A translation of Leonhard Euler's "On amicable numbers", arXiv:math/0409196 [math.HO], 2004-2009.
S. Chernykh, Amicable pairs list
E. B. Escott, Amicable numbers, Scripta Mathematica, 12 (1946), 61-72 [Annotated scanned copy]
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
Passawan Noppakaew and Prapanpong Pongsriiam, Product of Some Polynomials and Arithmetic Functions, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.
J. O. M. Pedersen, Known Amicable Pairs [Broken link]
J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]
T. Trotter, Jr., Amicable Numbers [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]
Eric Weisstein's World of Mathematics, Amicable Pair
FORMULA
a(n) = A259180(2n) = A180164(n) - A259180(2n-1) = A180164(n) - A002025(n). - Omar E. Pol, Jul 15 2015
MAPLE
f:= proc(t) uses numtheory; local s;
s:= sigma(t) - t; s > t and sigma(s) - s = t
end proc;
Am1:= select(f, [$1..10^6]);
map(numtheory:-sigma, Am1); # Robert Israel, Jul 16 2015
MATHEMATICA
amicableQ[n_] := With[{s = DivisorSigma[1, n] - n}, r = n != s && n == DivisorSigma[1, s] - s; If[r, mate[n] = s; True, False]]; mate /@ Select[ Range[lim], amicableQ[#] && # < mate[#] &] (* Jean-François Alcover, Sep 20 2011 *)
Table[DivisorSigma[1, A002025[n]] - A002025[n], {n, 50}] (* T. D. Noe, Sep 20 2011 *)
PROG
(PARI) aliquot(n)=sigma(n)-n
isA002046(n)={local(a); a=aliquot(n); a<n && aliquot(a)==n} \\ Michael B. Porter, Apr 17 2010
CROSSREFS
Sequence in context: A090789 A234970 A260087 * A339679 A339683 A343917
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)