A278919 Numbers n such that phi(n-2) divides sigma(n-1)+1.

3, 4, 5, 17, 26, 257, 65537, 4294967297

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 30 2016

Keywords

• nonn
• more
• hard

Comments

Numbers n such that A000010(n-2) divides A000203(n-1)+1.

Supersequence of Fermat primes (A019434).

Conjecture: this sequence is finite.

Any further terms are > 10^12. - Lucas A. Brown, Sep 22 2024

Examples

			3 is in this sequence because phi(1) divides sigma(2)+1; 1 divides 4.
4 is in this sequence because phi(2) divides sigma(3)+1; 1 divides 5.
5 is in this sequence because phi(3) divides sigma(4)+1; 2 divides 8.
17 is in this sequence because phi(15) divides sigma(16)+1; 8 divides 32.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A000010, A000203, A019434, A256439.

Programs

Magma

[3] cat [n: n in [4..10000000] | Denominator((SumOfDivisors(n-1)+1)/EulerPhi(n-2)) eq 1];

Mathematica

Select[Range[3,66000],Divisible[DivisorSigma[1,(#-1)]+1,EulerPhi[#-2]]&] (* Ivan N. Ianakiev, Dec 05 2016 *)

Extensions

a(8) from Ivan N. Ianakiev, Dec 05 2016