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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
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
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
Sequence in context: A190526 A141152 A372250 * A341476 A303190 A173142
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 07 2002
EXTENSIONS
More terms and entry revised by Sean A. Irvine, Oct 29 2023
STATUS
approved