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%I #27 Feb 18 2021 00:19:18
%S 19164,129357,14971875,45316123,434325391
%N Numbers that form a Pythagorean 6-tuple with their first four arithmetic derivatives.
%e First four arithmetic derivatives of 19164 are 25564, 31848, 58412, 61916 and sqrt(19164^2 + 25564^2 + 31848^2 + 58412^2 + 61916^2) = 96336.
%p with(numtheory);
%p Dr:=proc(w) local x,p; x:=w*add(op(2,p)/op(1,p),p=ifactors(w)[2]); end:
%p P:=proc(q,h) local a,b,k,n; for n from 2 to q do a:=n; b:=n^2;
%p for k from 1 to h do a:=Dr(a); b:=b+a^2; od; if type(sqrt(b),integer) then print(n);
%p fi; od; end: P(10^9,4);
%Y Cf. A003415, A210503, A230543, A249105, A249107, A249110.
%K nonn,more
%O 1,1
%A _Paolo P. Lava_, Oct 21 2014
%E a(4) from _Ray Chandler_, Dec 23 2016
%E a(5) from _Ray Chandler_, Jan 11 2017