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A300447 Numbers x such that sigma(x) = sigma(y), with x<>y, where y is the 10's complement mod 10 of the digits of x.

%I A300447 #17 Mar 19 2018 06:27:58
%S A300447 54,56,513,520,546,564,580,597,4845,5130,5223,5454,5656,5887,5970,
%T A300447 6265,44226,46365,48450,50260,50840,51300,52230,52520,53768,57342,
%U A300447 58580,58870,59700,62650,64745,66884,463650,477972,484500,489132,489632,493752,501536,503274
%N A300447 Numbers x such that sigma(x) = sigma(y), with x<>y, where y is the 10's complement mod 10 of the digits of x.
%H A300447 Paolo P. Lava, <a href="/A300447/b300447.txt">Table of n, a(n) for n = 1..150</a>
%e A300447 sigma(54) = sigma(56) = 120;
%e A300447 sigma(513) = sigma(597) = 800;
%e A300447 sigma(477972) = sigma(633138) = 1415232.
%p A300447 with(numtheory): P:=proc(q) local a,b,k,n;
%p A300447 for n from 1 to q do a:=convert(n,base,10);
%p A300447 for k from 1 to nops(a) do a[k]:=(10-a[k]) mod 10; od; b:=0;
%p A300447 for k from 1 to nops(a) do b:=b*10+a[nops(a)-k+1]; od;
%p A300447 if b<>n and sigma(b)=sigma(n) then print(n); fi; od; end: P(10^6);
%t A300447 Select[Range[10^6], Apply[And[#1 != #2, DivisorSigma[1, #1] == DivisorSigma[1, #2]] &, {#, FromDigits[IntegerDigits[#] /. d_?Positive :> 10 - d]}] &] (* _Michael De Vlieger_, Mar 09 2018 *)
%o A300447 (PARI) isok(x) = {my(dx = digits(x), dy = vector(#dx, k, (10-dx[k]) % 10), y = fromdigits(dy)); (x != y) && (sigma(x) == sigma(y));} \\ _Michel Marcus_, Mar 07 2018
%Y A300447 Cf. A000203, A055120.
%K A300447 nonn,base,easy
%O A300447 1,1
%A A300447 _Paolo P. Lava_, Mar 06 2018