A291199 Primes p such that phi(p*(p+1)/2) is a triangular number (A000217).

2477, 44287823, 58192759, 110369351, 664009019, 2574106333, 6870260119, 7423240007, 60370077539, 188271042191, 235399729007, 236767359977, 305214702643, 717724689959

Offset: 1

Author

Altug Alkan, Aug 20 2017

Keywords

• nonn
• more

Comments

a(15) > 10^12. - Giovanni Resta, Aug 21 2017

Examples

			Prime number 2477 is a term since phi(2477*2478/2) = 1856*1857/2.
		

Crossrefs

Cf. A000010, A000217, A034953, A086700.

Programs

PARI

isok(n) = isprime(n) && ispolygonal(eulerphi(n*(n+1)/2), 3);

PARI

is(n) = ispolygonal(eulerphi(n\2+1)*(n-1), 3) && isprime(n) \\ Charles R Greathouse IV, Aug 22 2017

Python

from _future_ import division
from sympy.ntheory.primetest import is_square
from sympy import totient, nextprime
A291199_list, p = [], 3
while p < 10**8:
    if is_square(8*(p-1)*totient((p+1)//2)+1):
        A291199_list.append(p)
    p = nextprime(p) # Chai Wah Wu, Aug 22 2017

Extensions

a(5)-a(14) from Giovanni Resta, Aug 21 2017