

A002046


Larger of amicable pair.
(Formerly M5435 N2363)


72



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
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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], 20042009.
S. Chernykh, Amicable pairs list
E. B. Escott, Amicable numbers, Scripta Mathematica, 12 (1946), 6172 [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 WaybackMachine]
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(2n1) = 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[#] &] (* JeanFrançois 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 * A339679 A339683 A343917
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



