The On-Line Encyclopedia of Integer Sequences (OEIS)

A180164 revision #24

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

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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

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

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}]