A247080 Numbers whose Euler totient is the reverse of the sum of its aliquot parts.

2, 735, 7665, 11505, 42630, 64578, 3440409, 11263073973

Offset: 1

Author

Paolo P. Lava, Nov 17 2014

Keywords

• nonn
• base
• more

Comments

Value of x such that phi(x) = Rev(sigma(x) - x).

a(9) > 2*10^11. - Hiroaki Yamanouchi, Nov 22 2014

a(9) > 10^13. - Giovanni Resta, Aug 26 2019

Examples

			phi(2) = 1 and sigma(2) - 2 = 1.
phi(735) = 336 and sigma(735) - 735 = 633.
phi(7665) = 3456 and sigma(7665) - 7665 = 6543.
		

Crossrefs

Cf. A000010, A001065, A069225, A254320.

Programs

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 phi(n)=T(sigma(n)-n) then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range[10^6], EulerPhi[#] == FromDigits[Reverse[IntegerDigits[DivisorSigma[1, #] - #]]] &] (* Michael De Vlieger, Jan 29 2015 *)

PARI

rev(n) = subst(Polrev(digits(n)), x, 10);
isok(n) = rev(sigma(n)-n) == eulerphi(n); \\ Michel Marcus, Jan 29 2015

Extensions

a(7)-a(8) from Hiroaki Yamanouchi, Nov 22 2014