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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 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 A081212 A280751 Adjacent sequences:  A308467 A308468 A308469 * A308471 A308472 A308473 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, May 29 2019 STATUS approved

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Last modified August 13 17:37 EDT 2022. Contains 356107 sequences. (Running on oeis4.)