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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..8.

Lucas A. Brown, Python program.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A000203, A019434, A256439.

Sequence in context: A173027 A290014 A298225 * A173061 A174326 A224890

Adjacent sequences: A278916 A278917 A278918 * A278920 A278921 A278922

Keyword

nonn,more,hard

Author

Juri-Stepan Gerasimov, Nov 30 2016

Extensions

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

Status

approved