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

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, 16, 40, 42, 20, 22, 46, 42, 20, 24, 52, 40, 24, 28, 58, 60, 30, 32, 48, 66, 32, 24, 70, 72, 36, 36, 60, 78, 32, 40, 82, 64, 42, 40, 88

Offset

1,3

Comments

This sequence gives the row length of the irregular triangle A337936 (complete system of tripling sequences modulo N(n)).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Lv Chuan, On the Mean Value of an Arithmetical Function, in Zhang Wenpeng (ed.), Research on Smarandache Problems in Number Theory (collected papers), 2004, pp. 89-92.

Formula

a(n) = A000010(A001651(n)) = phi(floor((3*n-1)/2)), for n >= 1.

a(n) ~ (9/(4*Pi^2))*n^2 + O(n^(3/2+eps)) (Lv Chuan, 2004). - Amiram Eldar, Aug 02 2022

Example

The pairs [n, N(n)], n >= 1, begin:
[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], ...

Mathematica

a[n_] := EulerPhi[Floor[(3*n - 1)/2]]; Array[a, 100] (* Amiram Eldar, Oct 22 2020 *)

Prog

(PARI) a(n) = eulerphi((3*n-1)\2); \\ Michel Marcus, Oct 22 2020

Crossrefs

Cf. A000010, A001651, A337936.

Sequence in context: A231655 A018841 A182043 * A138125 A098793 A083220

Adjacent sequences: A337934 A337935 A337936 * A337938 A337939 A337940

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 22 2020

Status

approved