A180164 The sum of the two numbers in an amicable pair, A002025(n) + A002046(n).

504, 2394, 5544, 10584, 12600, 21600, 26880, 35712, 139104, 133920, 138240, 157248, 168480, 224640, 262080, 245520, 294840, 311040, 348192, 357120, 388800, 399168, 645624, 698544, 749952, 756000, 892800, 955206, 1017792, 1048320

Offset

1,1

Comments

This sequence initially shares many terms with A161005 because small amicable pairs are sometimes consecutive terms in the sorted list of amicable numbers, A063990.

This sequence is sorted by the smaller (abundant) member from A002025, so a(n) is not increasing. - Jeppe Stig Nielsen, Jan 27 2015

Duplicates occur, e.g., a(32)=a(35)=1296000. - Jeppe Stig Nielsen, Jan 27 2015

Comment originally by M. F. Hasler, Dec 14 2013, in A161005: "Also: The common value of sigma(a) = sigma(b) of the amicable pairs (a,b). See A137231 for the analog for amicable triples, and A116148 for quadruples." - Jeppe Stig Nielsen, Jan 27 2015

It is not known if a(n) is always even (see Hagis links). - Jeppe Stig Nielsen, Jan 31 2015

Are all terms abundant (A005101)? The first 10000 terms are. - Ivan N. Ianakiev, Apr 15 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Peter Hagis, Lower bounds for relatively prime amicable numbers of opposite parity, Math. Comp. 24 (1970), 963-968.

Peter Hagis, Relatively Prime Amicable Numbers of Opposite Parity, Mathematics Magazine, Vol. 43, No. 1 (Jan., 1970), pp. 14-20.

Eric W. Weisstein's World of Mathematics, Pair Sum.

Formula

a(n) = A259180(2n-1) + A259180(2n). - Omar E. Pol, Oct 22 2017

Example

a(9) = A002025(9) + A002046(9) = 63020 + 76084 = 139104.

Mathematica

s[n_] := DivisorSigma[1, n]-n; smallAmicableQ[n_] := Module[{b=s[n]}, n<b && s[b]==n]; a=Select[Range[10^6], smallAmicableQ]; Table[n+s[n], {n, a}]

Crossrefs

Cf. A002025, A002046, A066539, A259180 (amicable pairs).

Sequence in context: A269038 A161005 A259953 * A263286 A061124 A141145

Adjacent sequences: A180161 A180162 A180163 * A180165 A180166 A180167

Keyword

nonn

Author

T. D. Noe, Aug 14 2010

Status

approved