A308470 - OEIS

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A308470

a(n) = (gcd(phi(n), 4*n^2 - 1) - 1)/2, where phi is A000010, Euler's totient function.

1

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 7, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 4, 7, 0, 1, 0, 0, 2, 0, 0, 0, 1, 3, 2, 0, 0, 1, 0, 2, 0, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,22

COMMENTS

2*a(n) + 1 = gcd(phi(2*n), (2*n - 1)*(2*n + 1)).

a(A000040(n)) = A099618(n).

Records occur at n = 1, 7, 22, 62, 172, 213, 372, 427, 473, ...

LINKS

Table of n, a(n) for n=1..95.

FORMULA

a(A000040(n)) = A099618(n).

a(A002476(n)) = 1.

a(A045309(n)) = 0.

EXAMPLE

a(7) = 1 because (gcd(phi(7), 4*7^2 - 1) - 1)/2 = (gcd(6, 195) - 1)/2 = (3 - 1)/2 = 1.

MATHEMATICA

Table[(GCD[EulerPhi[n], 4n^2 - 1] - 1)/2, {n, 100}] (* Alonso del Arte, May 30 2019 *)

PROG

(Magma) [(Gcd(EulerPhi(n), 4*n^2-1)-1)/2: n in [1..95]];

(Python)

from fractions import gcd

def A000010(n):

if n == 1:

return 1

d, m = 1, 0

while d < n:

if gcd(d, n) == 1:

m = m+1

d = d+1

return m

n = 0

while n < 30:

n = n+1

print(n, (gcd(A000010(n), 4*n**2-1)-1)//2) # A.H.M. Smeets, Aug 18 2019

CROSSREFS

Cf. A000010, A000040, A002476, A045309, A099618.

Sequence in context: A085983 A285701 A088183 * A070140 A361561 A081212

Adjacent sequences: A308467 A308468 A308469 * A308471 A308472 A308473

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, May 29 2019

STATUS

approved