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

1,1

Comments

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)

Links

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

Example

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002378, A002383, A359847.

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

Sequence in context: A137673 A226245 A369610 * A066271 A127594 A094604

Adjacent sequences: A236383 A236384 A236385 * A236387 A236388 A236389

Keyword

nonn,easy

Author

Joseph L. Pe, Jan 24 2014

Extensions

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

Status

approved