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A360944
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Numbers m such that phi(m) is a triangular number, where phi is the Euler totient function (A000010).
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2
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1, 2, 7, 9, 11, 14, 18, 22, 29, 37, 57, 58, 63, 67, 74, 76, 79, 108, 114, 126, 134, 137, 143, 155, 158, 175, 183, 191, 211, 225, 231, 244, 248, 274, 277, 286, 308, 310, 329, 341, 350, 366, 372, 379, 382, 396, 417, 422, 423, 450, 453, 462, 554, 556, 604, 623, 631, 658, 682
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OFFSET
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1,2
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COMMENTS
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Subsequence of primes is A055469 because in this case phi(k(k+1)/2+1) = k(k+1)/2.
Subsequence of triangular numbers is A287472.
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LINKS
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EXAMPLE
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phi(57) = 36 = 8*9/2, a triangular number; so 57 is a term of the sequence.
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MAPLE
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filter := m -> issqr(1 + 8*numtheory:-phi(m)) : select(filter, [$(1 .. 700)]);
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MATHEMATICA
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Select[Range[700], IntegerQ[Sqrt[8 * EulerPhi[#] + 1]] &] (* Amiram Eldar, Feb 27 2023 *)
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PROG
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(PARI) isok(m) = ispolygonal(eulerphi(m), 3); \\ Michel Marcus, Feb 27 2023
(Python)
from itertools import islice, count
from sympy.ntheory.primetest import is_square
from sympy import totient
def A360944_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:is_square((totient(n)<<3)+1), count(max(1, startvalue)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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