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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.

%I A066573 #13 Jul 30 2025 15:01:59
%S A066573 1,3,22,223,283,355,22,421,389,1065,365,1508,2130,3079,1065,69203,
%T A066573 51872,127539,83282,128604,152628,252271,191963,295294,130252,459590,
%U A066573 717615,1401314,2840,7189717,1258370,10269235,2130,11671711,11519862,19177306,17002972,21316045
%N 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.
%H A066573 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a066/A066573.java">Java program</a> (github)
%H A066573 J. Pe, <a href="https://vixra.org/abs/2503.0165">On a Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 168-172.
%e A066573 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.
%t A066573 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}]
%Y A066573 Cf. A066511, A066218.
%K A066573 nonn
%O A066573 1,2
%A A066573 _Joseph L. Pe_, Jan 07 2002
%E A066573 More terms and entry revised by _Sean A. Irvine_, Oct 29 2023