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Numbers k such that the reversal of phi(k) is sigma(k)-k.
1

%I #28 Sep 07 2024 03:21:26

%S 2,11,101,735,7665,11505,16459,64578,378871,541033,3440409,5639353,

%T 5230000213,5762782573,5828558173,8130408803,8275586723,9738107377,

%U 11263073973,37057275961,38914628453,58285958173,231243884637,350649946051,380047486211,516420024613,547083380743,576216622573

%N Numbers k such that the reversal of phi(k) is sigma(k)-k.

%e sigma(2) - 2 = 1; rev(1) = 1 = phi(2).

%e sigma(735) - 735 = 633; rev(633) = 336 = phi(735).

%p with(numtheory):T:=proc(w) local x,y,z; x:=w; y:=0;

%p for z from 1 to ilog10(x)+1 do 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 T(phi(n))=sigma(n)-n then print(n); fi; od; end: P(10^7);

%t Select[Range[564*10^4],IntegerReverse[EulerPhi[#]]==DivisorSigma[1,#]-#&] (* The program generates the first 12 terms of the sequence. *) (* _Harvey P. Dale_, Jul 03 2024 *)

%o (PARI) rev(n) = subst(Polrev(digits(n)), x, 10);

%o isok(n) = (sigma(n)-n) == rev(eulerphi(n)); \\ _Michel Marcus_, Jan 29 2015

%Y Cf. A000010, A000203, A001065, A069225, A247080.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Jan 28 2015

%E a(12) from _Michel Marcus_, Jan 29 2015

%E a(13)-a(28) from _Giovanni Resta_, May 08 2015