A291340 Primes p such that phi(p*(p-1)/2) is a triangular number (A000217).

2, 617, 11243, 72817, 134213, 1083601, 1301617, 669175321, 2759347757, 5023245823, 10904836391, 11230923643, 12828977503, 27741297781

Offset

1,1

Comments

Prime 2 followed by odd primes p such that either (i) p-1 == 2 (mod 4) belongs to A115910; or (ii) p-1 == 0 (mod 4) belongs to A256545. - Max Alekseyev, Sep 12 2025

Links

Table of n, a(n) for n=1..14.

Prog

(Python)
from __future__ import division
from sympy.ntheory.primetest import is_square
from sympy import totient, nextprime
A291340_list, p = [2], 3
while p < 10**6:
    if is_square(8*(p-1)*totient((p-1)//2)+1):
        A291340_list.append(p)
    p = nextprime(p)

Crossrefs

Inspired by A291199.

Cf. A000217, A115910, A256545.

Sequence in context: A281537 A134796 A120830 * A332162 A364070 A046856

Adjacent sequences: A291337 A291338 A291339 * A291341 A291342 A291343

Keyword

nonn,more

Author

Chai Wah Wu, Aug 31 2017

Status

approved