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A002046 Larger of amicable pair.
(Formerly M5435 N2363)
45
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

D. Moews, Perfect, amicable and sociable numbers

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

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-Fran├žois 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

Cf. A002025, A063990, A180164, A259180.

Sequence in context: A090789 A234970 A260087 * A143191 A180220 A108110

Adjacent sequences:  A002043 A002044 A002045 * A002047 A002048 A002049

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.