A278919 - OEIS

A278919

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

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

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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

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

KEYWORD

nonn,more,hard

AUTHOR

EXTENSIONS

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

STATUS

approved