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A337937 a(n) = Euler totient function phi = A000010 evaluated at N(n) = floor((3*n-1)/2) = A001651(n), for n >= 1.

%I A337937 #20 Aug 06 2024 07:24:45
%S A337937 1,1,2,4,6,4,4,10,12,6,8,16,18,8,10,22,20,12,12,28,30,16,16,24,36,18,
%T A337937 16,40,42,20,22,46,42,20,24,52,40,24,28,58,60,30,32,48,66,32,24,70,72,
%U A337937 36,36,60,78,32,40,82,64,42,40,88
%N A337937 a(n) = Euler totient function phi = A000010 evaluated at N(n) = floor((3*n-1)/2) =  A001651(n), for n >= 1.
%C A337937 This sequence gives the row length of the irregular triangle A337936 (complete system of tripling sequences modulo N(n)).
%H A337937 Amiram Eldar, <a href="/A337937/b337937.txt">Table of n, a(n) for n = 1..10000</a>
%H A337937 Lv Chuan, <a href="https://citeseerx.ist.psu.edu/pdf/134f67dafd17bab61928c5a02e2e9808a27a1dad">On the Mean Value of an Arithmetical Function</a>, in Zhang Wenpeng (ed.), Research on Smarandache Problems in Number Theory (collected papers), 2004, pp. 89-92.
%F A337937 a(n) = A000010(A001651(n)) = phi(floor((3*n-1)/2)), for n >= 1.
%F A337937 a(n) ~ (9/(4*Pi^2))*n^2 + O(n^(3/2+eps)) (Lv Chuan, 2004). - _Amiram Eldar_, Aug 02 2022
%e A337937 The pairs [n, N(n)], n >= 1, begin:
%e A337937 [1, 1], [2, 2], [3, 4], [4, 5], [5, 7], [6, 8], [7, 10], [8, 11], [9, 13], [10, 14], [11, 16], [12, 17], [13, 19], [14, 20], [15, 22], [16, 23], [17, 25], [18, 26], [19, 28], [20, 29], ...
%t A337937 a[n_] := EulerPhi[Floor[(3*n - 1)/2]]; Array[a, 100] (* _Amiram Eldar_, Oct 22 2020 *)
%o A337937 (PARI) a(n) = eulerphi((3*n-1)\2); \\ _Michel Marcus_, Oct 22 2020
%Y A337937 Cf. A000010, A001651, A337936.
%K A337937 nonn,easy
%O A337937 1,3
%A A337937 _Wolfdieter Lang_, Oct 22 2020