A117296 -id:A117296 - cp's OEIS frontend

A236386 Numbers m such that phi(m) is an oblong number.

3, 4, 6, 7, 9, 13, 14, 18, 21, 25, 26, 28, 31, 33, 36, 42, 43, 44, 49, 50, 62, 66, 73, 86, 87, 91, 95, 98, 111, 116, 117, 121, 135, 146, 148, 152, 157, 161, 169, 174, 182, 190, 201, 207, 211, 216, 222, 228, 234, 237, 241, 242, 252, 268, 270, 287, 289, 305

Offset: 1

Joseph L. Pe, Jan 24 2014

An oblong number (A002378) is of the form k*(k+1) where k is a natural number.
From Bernard Schott, Feb 27 2023: (Start)
Subsequence of primes is A002383 because in this case phi(k^2+k+1) = k*(k+1).
Subsequence of oblong numbers is A359847 where k and phi(k) are both oblong numbers. (End)

			phi(13) = 12 = 3*4, an oblong number; so 13 is a term of the sequence.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000010, A002378, A002383, A359847.

Similar, but where phi(m) is: A039770 (square), A039771 (cube), A078164 (biquadrate), A096503 (repdigit), A117296 (palindrome), A360944 (triangular).

filter := m -> issqr(1 + 4*phi(m)) : select(filter, [$(1 .. 700)]); # Bernard Schott, Feb 26 2023

Select[Range[500], IntegerQ@Sqrt[1 + 4*EulerPhi[#]] &] (* Giovanni Resta, Jan 24 2014 *)

isok(m) = my(t=eulerphi(m)); !(t%2) && ispolygonal(t/2, 3); \\ Michel Marcus, Feb 27 2023

from itertools import count, islice
from sympy.ntheory.primetest import is_square
from sympy import totient
def A236386_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:is_square((totient(n)<<2)+1), count(max(1,startvalue)))
A236386_list = list(islice(A236386_gen(),20)) # Chai Wah Wu, Feb 28 2023

a(16)-a(58) from Giovanni Resta, Jan 24 2014

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

Original entry on oeis.org

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

Bernard Schott, Feb 26 2023

nonn

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.

			phi(57) = 36 = 8*9/2, a triangular number; so 57 is a term of the sequence.

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

Cf. A000010, A000217, A055469, A287472.

Similar, but with phi(m) is: A039770 (square), A078164 (biquadrate), A096503 (repdigit), A117296 (palindrome), A236386 (oblong).

filter := m ->  issqr(1 + 8*numtheory:-phi(m)) : select(filter, [$(1 .. 700)]);

Select[Range[700], IntegerQ[Sqrt[8 * EulerPhi[#] + 1]] &] (* Amiram Eldar, Feb 27 2023 *)

isok(m) = ispolygonal(eulerphi(m), 3); \\ Michel Marcus, Feb 27 2023

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

cp's OEIS Frontend

A236386 Numbers m such that phi(m) is an oblong number.

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