A254320 Numbers k such that the reversal of phi(k) is sigma(k)-k.
2, 11, 101, 735, 7665, 11505, 16459, 64578, 378871, 541033, 3440409, 5639353, 5230000213, 5762782573, 5828558173, 8130408803, 8275586723, 9738107377, 11263073973, 37057275961, 38914628453, 58285958173, 231243884637, 350649946051, 380047486211, 516420024613, 547083380743, 576216622573
Offset: 1
Examples
sigma(2) - 2 = 1; rev(1) = 1 = phi(2). sigma(735) - 735 = 633; rev(633) = 336 = phi(735).
Programs
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Maple
with(numtheory):T:=proc(w) local x,y,z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end: P:=proc(q) local n; for n from 1 to q do if T(phi(n))=sigma(n)-n then print(n); fi; od; end: P(10^7);
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Mathematica
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 *)
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PARI
rev(n) = subst(Polrev(digits(n)), x, 10); isok(n) = (sigma(n)-n) == rev(eulerphi(n)); \\ Michel Marcus, Jan 29 2015
Extensions
a(12) from Michel Marcus, Jan 29 2015
a(13)-a(28) from Giovanni Resta, May 08 2015