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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.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 22 2020
STATUS
approved