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A210935 Numbers n for which n*n'/(n+n') is an integer, where n' is the arithmetic derivative of n.

%I A210935 #20 Jan 26 2013 03:00:30
%S A210935 1,4,64,80,108,270,351,432,729,768,864,2916,5184,5832,6250,6912,12096,
%T A210935 13500,16384,25600,32832,34992,37500,39366,43200,46656,50000,73008,
%U A210935 74304,81648,84375,110592,131250,138240,143748,153664,172800,176418,200000,225000
%N A210935 Numbers n for which n*n'/(n+n') is an integer, where n' is the arithmetic derivative of n.
%C A210935 Only eleven odd numbers in the first 150 terms: a(1)=1, a(7)=351, a(9)=729, a(31)=84375, a(76)=2470629, a(78)=2709375, a(87)=4159375, a(89)=4348377, a(115)=13286025, a(126)=22235661, a(128)=25059375.
%H A210935 Paolo P. Lava and Donovan Johnson, <a href="/A210935/b210935.txt">Table of n, a(n) for n = 1..500</a> (first 150 terms from Paolo P. Lava)
%e A210935 n=729; n'=1458; n*n'/(n+n')=486.
%p A210935 with(numtheory);
%p A210935 A210935:= proc(n)
%p A210935 local a,i,p,pfs;
%p A210935 for i from 1 to n do
%p A210935     pfs:=ifactors(i)[2];  a:=i*add(op(2,p)/op(1,p),p=pfs) ;
%p A210935     if a*i/(a+i)=trunc(a*i/(a+i)) then print(i); fi;
%p A210935 od; end:
%p A210935 A210935(100000000);
%Y A210935 Cf. A003415, A165562.
%K A210935 nonn
%O A210935 1,2
%A A210935 _Paolo P. Lava_, May 11 2012