A162884 Half the difference between the larger and smaller term of the n-th amicable pair.

32, 13, 152, 272, 68, 56, 1155, 560, 6532, 32, 2025, 9009, 4490, 11835, 8775, 392, 5756, 13210, 2240, 2288, 9032, 2860, 42272, 40652, 55426, 21592, 8944, 8575, 5840, 1755, 34648, 38072, 33536, 38296, 4664, 57796, 35296, 30555, 10856, 41384, 88965, 22496

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 16 2009

Keywords

• nonn

Examples

			a(7)=1155 because the 7th pair of amicable numbers is 12285 and 14595; and (14595-12285)/2=1155.
		

Crossrefs

Cf. A063990, A066539, A259180.

Programs

Maple

read("transforms3") ; L002046 := BFILETOLIST("b002046.txt") : L002025 := BFILETOLIST("b002025.txt") : A066539 := proc(n) global L002046,L002025; op(n,L002046)-op(n,L002025) ; end:
A162884 := proc(n) A066539(n)/2 ; end: seq(A162884(n),n=1..100) ; # R. J. Mathar, Jul 19 2009

Mathematica

With[{s = PositionIndex@ Array[DivisorSigma[1, #] &, 10^6]}, Flatten@ Map[Differences, Apply[Join, Map[Function[n, Select[Subsets[Lookup[s, n], {2}], Total@ # == n &]], Sort@ Select[Keys@ s, Length@ Lookup[s, #] > 1 &]]]]/2] (* Michael De Vlieger, Oct 26 2017 *)

Formula

a(n) = A066539(n)/2.

a(n) = (A259180(2n) - A259180(2n-1))/2. - Omar E. Pol, Oct 26 2017

Extensions

Terms resorted along with A066539 by R. J. Mathar, Jul 19 2009