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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.
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%I #11 Oct 29 2023 17:28:38

%S 1,3,22,223,283,355,22,421,389,1065,365,1508,2130,3079,1065,69203,

%T 51872,127539,83282,128604,152628,252271,191963,295294,130252,459590,

%U 717615,1401314,2840,7189717,1258370,10269235,2130,11671711,11519862,19177306,17002972,21316045

%N 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 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a066/A066573.java">Java program</a> (github)

%H J. Pe, <a href="http://www.numeratus.net/fperfect/fperfect.html">On a Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 168-172.

%e 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 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 Cf. A066511, A066218.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Jan 07 2002

%E More terms and entry revised by _Sean A. Irvine_, Oct 29 2023