A002046 Larger of amicable pair.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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
• David Moews, Perfect, amicable and sociable numbers
• 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
• Eric Weisstein's World of Mathematics, Amicable Pair

Crossrefs

Cf. A002025, A063990, A180164, A259180.

Programs

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 *)

PARI

aliquot(n)=sigma(n)-n
isA002046(n)={if (n>1, local(a);a=aliquot(n);aMichael B. Porter, Apr 17 2010

Formula

a(n) = A259180(2n) = A180164(n) - A259180(2n-1) = A180164(n) - A002025(n). - Omar E. Pol, Jul 15 2015

Extensions

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