A358039 a(n) is the Euler totient function phi applied to the n-th cubefree number.

1, 1, 2, 2, 4, 2, 6, 6, 4, 10, 4, 12, 6, 8, 16, 6, 18, 8, 12, 10, 22, 20, 12, 12, 28, 8, 30, 20, 16, 24, 12, 36, 18, 24, 40, 12, 42, 20, 24, 22, 46, 42, 20, 32, 24, 52, 40, 36, 28, 58, 16, 60, 30, 36, 48, 20, 66, 32, 44, 24, 70, 72, 36, 40, 36, 60, 24, 78, 40

Offset

1,3

Comments

The analogous sequence with squarefree numbers is A049200.

Links

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

Zhu Weiyi, On the cube free number sequences, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.

Formula

a(n) = A000010(A004709(n)).

Sum_{k=1..n} a(k) = (c/(2*zeta(3)))*n^2 + O(n^(3/2+eps)), where c = Product_{p prime} (1 - (p+1)/(p^3+p^2+1)) = 0.62583324412633345811... (Weiyi, 2004).

From Amiram Eldar, Oct 09 2023: (Start)

Sum_{n>=1} 1/(A004709(n)*a(n)) = Product_{p prime} (1 + (p^2+1)/((p-1)*p^3)) = 2.14437852780769816048... .

Sum_{n>=1} 1/a(n)^2 = Product_{p prime} (1 + (p^2+1)/((p-1)^2*p^2)) = 3.26032746607943673536... . (End)

Mathematica

EulerPhi[Select[Range[100], Max[FactorInteger[#][[;; , 2]]] < 3 &]]

Crossrefs

Cf. A000010, A002117, A004709, A049200, A358040.

Sequence in context: A236628 A078429 A360523 * A171751 A124676 A076249

Adjacent sequences: A358036 A358037 A358038 * A358040 A358041 A358042

Keyword

nonn

Author

Amiram Eldar, Oct 29 2022

Status

approved