A037225 a(n) = phi(2n+1).
1, 2, 4, 6, 6, 10, 12, 8, 16, 18, 12, 22, 20, 18, 28, 30, 20, 24, 36, 24, 40, 42, 24, 46, 42, 32, 52, 40, 36, 58, 60, 36, 48, 66, 44, 70, 72, 40, 60, 78, 54, 82, 64, 56, 88, 72, 60, 72, 96, 60, 100, 102, 48, 106, 108, 72, 112, 88, 72, 96, 110, 80, 100, 126, 84, 130
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..10000
- John Brillhart, J. S. Lomont, and Patrick Morton, Cyclotomic properties of the Rudin-Shapiro polynomials, J. Reine Angew. Math. 288 (1976), 37-65; see Table 2; MR0498479 (58 #16589). - From _N. J. A. Sloane_, Jun 06 2012
- V. I. Levenshtein, Conflict-avoiding codes and cyclic triple systems, Problemy Peredachi Informatsii, 43 (No. 3, 2007), 39-53 (in Russian).
- V. I. Levenshtein, Conflict-avoiding codes and cyclic triple systems, Problems of Information. Transmission, 43 (2007), 199-212 (translation from Russian).
- N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence).
- Wikipedia, Lehmer's totient problem.
Programs
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Magma
[EulerPhi(2*n+1): n in [0..70]]; // Vincenzo Librandi, Jul 16 2019
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Mathematica
Table[EulerPhi[2 n + 1], {n, 0, 80}] (* Vincenzo Librandi, Jul 16 2019 *) -
PARI
a(n) = eulerphi(2*n+1) \\ Amiram Eldar, Nov 17 2022
Formula
Sum_{k=0..n} a(k) ~ c * n^2, where c = 8/Pi^2 = 0.810569... (A217739). - Amiram Eldar, Nov 17 2022
a(n) = 2*n iff 2*n+1 is prime, see A005097. - Alain Rocchelli, Jun 22 2023
From Peter Bala, Feb 01 2024: (Start)
Odd bisection of A000010.
a(n) = 2*A072451(n) for n >= 1.
G.f.: Sum_{n >= 1} phi(2*n+1)*x^(2*n+1) = Sum_{n >= 1} moebius(n)*x^(2*n-1)*(1 + x^(4*n-2))/(1 - x^(4*n-2))^2 = x + 2*x^3 + 4*x^5 + 6*x^7 + 6*x^9 + .... (End)
Comments