login
Numbers n such that phi(n) = sigma(n) - reversal(sigma(n)).
2

%I #18 Feb 05 2014 10:37:18

%S 19,199,437,603,1999,12834,16348,21293,22183,23383,25273,27263,44377,

%T 46367,199999,670661,691351,803851,845321,1425650,2103643,2111191,

%U 2123893,2174143,2543773,2552723,2753713,3791659,4003997,4034347,4133332,4223887,4244287,4492429,4663667

%N Numbers n such that phi(n) = sigma(n) - reversal(sigma(n)).

%C A prime p is in the sequence iff p is of the form 2*10^m-1. 19, 199, 1999 are such terms of the sequence.

%C If both numbers p=2*10^m-1 and q=2*10^m+3 are prime then n=p*q is in the sequence. For m=1, 3, 5, 7 both p and q are prime.

%C If both numbers p=2*10^m-1 and q=(7*10^m-1)/3 are prime then n=p*q is in the sequence. For m=1, 2, 3, 53 both p and q are prime.

%H Giovanni Resta, <a href="/A230012/b230012.txt">Table of n, a(n) for n = 1..103</a> (terms < 10^11)

%t r[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Do[If[DivisorSigma[1,n]- r[DivisorSigma[1,n]]==EulerPhi[n],Print[n]],{n,15000000}]

%Y Cf. A000010, A000203, A004086, A069225, A237257.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Feb 04 2014