cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A270778 Primes p such that sigma(p-1) - phi(p-1) = (3p-5)/2.

This page as a plain text file.
%I A270778 #25 Sep 08 2022 08:46:16
%S A270778 3,5,11,17,257,65537,119831
%N A270778 Primes p such that sigma(p-1) - phi(p-1) = (3p-5)/2.
%C A270778 Primes p such that A051612(p-1) = (3p-5)/2.
%C A270778 Fermat primes from A019434 are terms.
%C A270778 If a(8) exists, it must be larger than 10^10.
%C A270778 Prime terms from A270836.
%C A270778 Necessary condition: sigma_-1(p-1) < 2. Thus a(n)-1 is a deficient number and a(n) = 2 mod 3 for n > 1. - _Charles R Greathouse IV_, Apr 01 2016
%C A270778 If a(8) exists, it must be larger than 10^11. - _Charles R Greathouse IV_, Apr 01 2016
%C A270778 If a(8) exists, it must be larger than 10^13. - _Giovanni Resta_, Apr 11 2016
%e A270778 17 is a term because sigma(16)-phi(16) = 31-8 = 23 = (3*17-5)/2.
%t A270778 Select[Prime@ Range[10^6], DivisorSigma[1, # - 1] - EulerPhi[# - 1] == (3 # - 5)/2 &] (* _Michael De Vlieger_, Mar 23 2016 *)
%o A270778 (Magma) [n: n in[1..10^7] | IsPrime(n) and 2*(SumOfDivisors(n-1) - EulerPhi(n-1)) eq 3*n-5]
%o A270778 (PARI) lista(nn) = forprime(p=2, nn, if (sigma(p-1) - eulerphi(p-1) == (3*p-5)/2, print1(p, ", "))); \\ _Michel Marcus_, Mar 23 2016
%o A270778 (PARI) is(n)=my(f=factor(n-1)); sigma(f) - eulerphi(f) == (3*n-5)/2 && isprime(n) \\ _Charles R Greathouse IV_, Apr 01 2016
%Y A270778 Cf. A000010, A000203, A051612, A270779, A270836.
%K A270778 nonn,more
%O A270778 1,1
%A A270778 _Jaroslav Krizek_, Mar 22 2016