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Numbers n such that sigma(n) = 2*(phi(n-1)+1).
2

%I #19 Sep 08 2022 08:46:11

%S 3,5,17,26,257,65537,10866583226

%N Numbers n such that sigma(n) = 2*(phi(n-1)+1).

%C Subsequence of A256439. Supersequence of Fermat primes (A019434).

%C a(8) > 10^13. - _Giovanni Resta_, Jul 13 2015

%e 17 is in the sequence because sigma(17) = 18 = 2*(phi(16-1)+1) = 2*9.

%t Select[Range@ 100000, DivisorSigma[1, #] == 2 (EulerPhi[# - 1] + 1) &] (* _Michael De Vlieger_, Mar 31 2015 *)

%o (Magma) Set(Sort([n: n in [2..1000000] | SumOfDivisors(n) / (EulerPhi(n-1) + 1) eq 2 ]))

%o (PARI) first(m)={ my(v=vector(m),i,r);r=0;for(i=1,m,until(sigma(r)===2*(eulerphi(r-1)+1),r++);v[i]=r;print1(r,", "););v;} _Anders Hellström_, Jul 29 2015

%Y Cf. A000010, A000203, A256439.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Mar 31 2015

%E a(7) from _Giovanni Resta_, Jul 13 2015