A066573 Pairs (x, y), x < y, of f-amicable numbers where f(k) = floor(|k*sin(k)|) sorted by increasing y, then increasing x; f-amicable numbers are defined in A066511.

1, 3, 22, 223, 283, 355, 22, 421, 389, 1065, 365, 1508, 2130, 3079, 1065, 69203, 51872, 127539, 83282, 128604, 152628, 252271, 191963, 295294, 130252, 459590, 717615, 1401314, 2840, 7189717, 1258370, 10269235, 2130, 11671711, 11519862, 19177306, 17002972, 21316045

Offset: 1

Author

Joseph L. Pe, Jan 07 2002

Keywords

• nonn

Examples

			Proper divisors of 22 are {1,2,11}; f applied to these = {0, 1, 10}, which sum to 11 = f(223). Proper divisors of 223 are {1}; f applied to these = {0}, which sum to 0 = f(22). Hence (22,223) is an f-amicable pair.
		

Links

• Sean A. Irvine, Java program (github)
• J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

Crossrefs

Cf. A066511, A066218.

Programs

Mathematica

f[x_] := Floor[Abs[x*Sin[x]]]; d[x_] := Apply[ Plus, Map[ f, Divisors[ x] ] ] - f[ x]; m = Table[{x, y}, {x, 1, 1000}, {y, 1, 1000}]; Do[a = m[[i, j]]; If[ (a[[1]] < a[[2]]) && (f[a[[1]]] == d[a[[2]]]) && (f[a[[2]]] == d[a[[1]]]), Print[{i, j}]], {j, 1, 1000}, {i, 1, 1000}]

Extensions

More terms and entry revised by Sean A. Irvine, Oct 29 2023