A270836 -id:A270836 - cp's OEIS frontend

A270837 Numbers k such that sigma(k-1) + phi(k-1) = (5*k-7)/2.

3, 5, 7, 9, 17, 33, 65, 67, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 5606129563

Offset: 1

Jaroslav Krizek, Mar 23 2016

nonn

Numbers k such that A065387(k-1) = (5*k-7)/2.
Numbers of the form 2^k + 1 for k >= 1 from A000051 are terms.
Prime terms are in A270779.

			17 is a term because sigma(16)+phi(16) = 31+8 = 39 = (5*17-7)/2.

Giovanni Resta, Table of n, a(n) for n = 1..47 (terms < 10^13)

Cf. A000010, A000051, A000203, A065387, A270779, A270836.

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

Select[Range[10^6], DivisorSigma[1, # - 1] + EulerPhi[# - 1] == (5 # - 7)/2 &] (* Michael De Vlieger, Mar 24 2016 *)

lista(nn) = {for(n=2, nn, if(sigma(n-1) + eulerphi(n-1) == (5*n-7)/2, print1(n, ", "))); } \\ Altug Alkan, Mar 23 2016

a(29)-a(31) from Michel Marcus, Apr 05 2016

a(32)-a(35) from Giovanni Resta, Apr 11 2016

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

Original entry on oeis.org

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

Offset: 1

Jaroslav Krizek, Mar 22 2016

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

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

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

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

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

lista(nn) = forprime(p=2, nn, if (sigma(p-1) - eulerphi(p-1) == (3*p-5)/2, print1(p, ", "))); \\ Michel Marcus, Mar 23 2016

is(n)=my(f=factor(n-1)); sigma(f) - eulerphi(f) == (3*n-5)/2 && isprime(n) \\ Charles R Greathouse IV, Apr 01 2016

cp's OEIS Frontend

A270837 Numbers k such that sigma(k-1) + phi(k-1) = (5*k-7)/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

PARI

PARI