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