A360944 Numbers m such that phi(m) is a triangular number, where phi is the Euler totient function (A000010).

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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000010, A000217, A055469, A287472.

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

Adjacent sequences: A360941 A360942 A360943 * A360945 A360946 A360947

Keyword

nonn

Author

Bernard Schott, Feb 26 2023

Status

approved