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%I #14 Sep 08 2022 08:46:18
%S 3,4,5,17,26,257,65537,4294967297
%N Numbers n such that phi(n-2) divides sigma(n-1)+1.
%C Numbers n such that A000010(n-2) divides A000203(n-1)+1.
%C Supersequence of Fermat primes (A019434).
%C Conjecture: this sequence is finite.
%e 3 is in this sequence because phi(1) divides sigma(2)+1; 1 divides 4.
%e 4 is in this sequence because phi(2) divides sigma(3)+1; 1 divides 5.
%e 5 is in this sequence because phi(3) divides sigma(4)+1; 2 divides 8.
%e 17 is in this sequence because phi(15) divides sigma(16)+1; 8 divides 32.
%t Select[Range[3,66000],Divisible[DivisorSigma[1,(#-1)]+1,EulerPhi[#-2]]&] (* _Ivan N. Ianakiev_, Dec 05 2016 *)
%o (Magma) [3] cat [n: n in [4..10000000] | Denominator((SumOfDivisors(n-1)+1)/EulerPhi(n-2)) eq 1];
%Y Cf. A000010, A000203, A019434, A256439.
%K nonn,more
%O 1,1
%A _Juri-Stepan Gerasimov_, Nov 30 2016
%E a(8) from _Ivan N. Ianakiev_, Dec 05 2016
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