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 A291199 Primes p such that phi(p*(p+1)/2) is a triangular number (A000217). 1
 2477, 44287823, 58192759, 110369351, 664009019, 2574106333, 6870260119, 7423240007, 60370077539, 188271042191, 235399729007, 236767359977, 305214702643, 717724689959 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(15) > 10^12. - Giovanni Resta, Aug 21 2017 LINKS EXAMPLE Prime number 2477 is a term since phi(2477*2478/2) = 1856*1857/2. PROG (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 CROSSREFS Cf. A000010, A000217, A034953, A086700. Sequence in context: A020411 A124594 A241048 * A260766 A003917 A235763 Adjacent sequences:  A291196 A291197 A291198 * A291200 A291201 A291202 KEYWORD nonn,more AUTHOR Altug Alkan, Aug 20 2017 EXTENSIONS a(5)-a(14) from Giovanni Resta, Aug 21 2017 STATUS approved

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Last modified May 27 01:53 EDT 2022. Contains 354092 sequences. (Running on oeis4.)