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

3, 5, 11, 17, 257, 65537, 119831

Offset: 1

Author

Jaroslav Krizek, Mar 22 2016

Keywords

• nonn
• more

Comments

Primes p such that A051612(p-1) = (3p-5)/2.

Fermat primes from A019434 are terms.

If a(8) exists, it must be larger than 10^10.

Prime terms from A270836.

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

If a(8) exists, it must be larger than 10^11. - Charles R Greathouse IV, Apr 01 2016

If a(8) exists, it must be larger than 10^13. - Giovanni Resta, Apr 11 2016

Examples

			17 is a term because sigma(16)-phi(16) = 31-8 = 23 = (3*17-5)/2.
		

Crossrefs

Cf. A000010, A000203, A051612, A270779, A270836.

Programs

Magma

[n: n in[1..10^7] | IsPrime(n) and 2*(SumOfDivisors(n-1) - EulerPhi(n-1)) eq 3*n-5]

Mathematica

Select[Prime@ Range[10^6], DivisorSigma[1, # - 1] - EulerPhi[# - 1] == (3 # - 5)/2 &] (* Michael De Vlieger, Mar 23 2016 *)

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

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