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A360944 Numbers m such that phi(m) is a triangular number, where phi is the Euler totient function (A000010). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
EXAMPLE
phi(57) = 36 = 8*9/2, a triangular number; so 57 is a term of the sequence.
MAPLE
filter := m -> issqr(1 + 8*numtheory:-phi(m)) : select(filter, [$(1 .. 700)]);
MATHEMATICA
Select[Range[700], IntegerQ[Sqrt[8 * EulerPhi[#] + 1]] &] (* Amiram Eldar, Feb 27 2023 *)
PROG
(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)))
A360944_list = list(islice(A360944_gen(), 20)) # Chai Wah Wu, Feb 28 2023
CROSSREFS
Similar, but with phi(m) is: A039770 (square), A078164 (biquadrate), A096503 (repdigit), A117296 (palindrome), A236386 (oblong).
Sequence in context: A191263 A287359 A022424 * A136498 A297826 A288598
KEYWORD
nonn
AUTHOR
Bernard Schott, Feb 26 2023
STATUS
approved

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Last modified May 27 16:57 EDT 2024. Contains 372880 sequences. (Running on oeis4.)