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.

440, 568, 2368, 2420, 5240, 5848, 10040, 11128, 12464, 12736, 21488, 21712, 24570, 29190, 34592, 36832, 126040, 133856, 133984, 134190, 139230, 142290, 152168, 159500, 175266, 177460, 200970, 244530, 244736, 246304, 248310, 279630, 283328, 284620, 306352, 337460

Offset: 1

Author

Michel Lagneau, Dec 19 2016

Keywords

• nonn

Comments

"Pseudo-amicable" numbers: pairs of numbers (x, y) such that A091818(x) = y and A091818(y) = x.

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.

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.

For ordered pairs see A279950.

Examples

			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.
		

Crossrefs

Cf. A063990, A074400, A091818, A279950.

Programs

Mathematica

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[#]&]