cp's OEIS Frontend

A279812 Let s(k) denote the sum of the even proper divisors of k. The sequence lists the pairs of numbers (x, y) such that s(x) = y and s(y) = x.

%I A279812 #11 Dec 24 2016 11:12:15
%S A279812 440,568,2368,2420,5240,5848,10040,11128,12464,12736,21488,21712,
%T A279812 24570,29190,34592,36832,126040,133856,133984,134190,139230,142290,
%U A279812 152168,159500,175266,177460,200970,244530,244736,246304,248310,279630,283328,284620,306352,337460
%N A279812 Let s(k) denote the sum of the even proper divisors of k. The sequence lists the pairs of numbers (x, y) such that s(x) = y and s(y) = x.
%C A279812 "Pseudo-amicable" numbers: pairs of numbers (x, y) such that A091818(x) = y and A091818(y) = x.
%C A279812 A pair of numbers x and y is called "pseudo-amicable" if the sum of the proper even divisors of either one is equal to the other. The smallest pair is x = 440, y = 568.
%C A279812 The sequence lists the numbers in increasing order. Note that the pairs (x, y) are not adjacent to each other in the list. For instance, the pair (126040, 152168) are "pseudo-amicable" numbers.
%C A279812 For ordered pairs see A279950.
%e A279812 The pair (a(1), a(2)) = (440, 568) is in the sequence because the even proper divisors of 440 are 2, 4, 8, 10, 20, 22, 40, 44, 88, 110, 220 with sum = 568 and the proper divisors of 568 are 2, 4, 8, 142, 284 with sum = 440.
%t A279812 s[n_]:=2*(DivisorSigma[1,n/2]-n/2);P[n_]:=If[Nest[s,n,2]==n&&!s[n]==n,True,False];Select[Range[10^6],P[#]&]
%Y A279812 Cf. A063990, A074400, A091818, A279950.
%K A279812 nonn
%O A279812 1,1
%A A279812 _Michel Lagneau_, Dec 19 2016