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

%I A291199 #24 Aug 22 2017 21:06:38
%S A291199 2477,44287823,58192759,110369351,664009019,2574106333,6870260119,
%T A291199 7423240007,60370077539,188271042191,235399729007,236767359977,
%U A291199 305214702643,717724689959
%N A291199 Primes p such that phi(p*(p+1)/2) is a triangular number (A000217).
%C A291199 a(15) > 10^12. - _Giovanni Resta_, Aug 21 2017
%e A291199 Prime number 2477 is a term since phi(2477*2478/2) = 1856*1857/2.
%o A291199 (PARI) isok(n) = isprime(n) && ispolygonal(eulerphi(n*(n+1)/2), 3);
%o A291199 (PARI) is(n) = ispolygonal(eulerphi(n\2+1)*(n-1), 3) && isprime(n) \\ _Charles R Greathouse IV_, Aug 22 2017
%o A291199 (Python)
%o A291199 from __future__ import division
%o A291199 from sympy.ntheory.primetest import is_square
%o A291199 from sympy import totient, nextprime
%o A291199 A291199_list, p = [], 3
%o A291199 while p < 10**8:
%o A291199     if is_square(8*(p-1)*totient((p+1)//2)+1):
%o A291199         A291199_list.append(p)
%o A291199     p = nextprime(p) # _Chai Wah Wu_, Aug 22 2017
%Y A291199 Cf. A000010, A000217, A034953, A086700.
%K A291199 nonn,more
%O A291199 1,1
%A A291199 _Altug Alkan_, Aug 20 2017
%E A291199 a(5)-a(14) from _Giovanni Resta_, Aug 21 2017