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

1,2

Links

Table of n, a(n) for n=1..38.

Sean A. Irvine, Java program (github)

J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

Example

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.

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}]

Crossrefs

Cf. A066511, A066218.

Sequence in context: A079489 A190526 A141152 * A341476 A303190 A173142

Adjacent sequences: A066570 A066571 A066572 * A066574 A066575 A066576

Keyword

nonn

Author

Joseph L. Pe, Jan 07 2002

Extensions

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

Status

approved