|
%I #33 Aug 26 2019 04:51:18
%S 2,735,7665,11505,42630,64578,3440409,11263073973
%N Numbers whose Euler totient is the reverse of the sum of its aliquot parts.
%C Value of x such that phi(x) = Rev(sigma(x) - x).
%C a(9) > 2*10^11. - _Hiroaki Yamanouchi_, Nov 22 2014
%C a(9) > 10^13. - _Giovanni Resta_, Aug 26 2019
%e phi(2) = 1 and sigma(2) - 2 = 1.
%e phi(735) = 336 and sigma(735) - 735 = 633.
%e phi(7665) = 3456 and sigma(7665) - 7665 = 6543.
%p with(numtheory): T:=proc(w) local x,y,z; x:=w; y:=0;
%p for z from 1 to ilog10(x)+1 do
%p y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
%p P:=proc(q) local n; for n from 1 to q do
%p if phi(n)=T(sigma(n)-n) then print(n); fi; od; end: P(10^9);
%t Select[Range[10^6], EulerPhi[#] == FromDigits[Reverse[IntegerDigits[DivisorSigma[1, #] - #]]] &] (* _Michael De Vlieger_, Jan 29 2015 *)
%o (PARI) rev(n) = subst(Polrev(digits(n)), x, 10);
%o isok(n) = rev(sigma(n)-n) == eulerphi(n); \\ _Michel Marcus_, Jan 29 2015
%Y Cf. A000010, A001065, A069225, A254320.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Nov 17 2014
%E a(7)-a(8) from _Hiroaki Yamanouchi_, Nov 22 2014
| 