A086700 Euler phi function applied to the triangular numbers.

1, 2, 2, 4, 8, 12, 12, 12, 24, 40, 20, 24, 72, 48, 32, 64, 96, 108, 72, 48, 120, 220, 88, 80, 240, 216, 108, 168, 224, 240, 240, 160, 320, 384, 144, 216, 648, 432, 192, 320, 480, 504, 420, 240, 528, 1012, 368, 336, 840, 640, 384, 624, 936, 720, 480, 432, 1008, 1624, 464, 480, 1800, 1080, 576, 768, 960, 1320

Offset: 1

Author

Jon Perry, Jul 28 2003

Keywords

• nonn
• easy

Examples

			a(3) = phi(6) = 2.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A000217, A065474.

Programs

Maple

with(numtheory):with(combinat):a:=n->phi(binomial(n,2)): seq(a(n), n=2..31); # Zerinvary Lajos, Oct 05 2007

Mathematica

EulerPhi[Accumulate[Range[70]]] (* Harvey P. Dale, Sep 16 2012 *)

PARI

vector(66,n,eulerphi(n*(n+1)/2))

Sage

[euler_phi(binomial(n,2)) for n in range(2,32)] # Zerinvary Lajos, Jun 06 2009

Formula

a(n) = A000010(A000217(n)). - Michel Marcus, Aug 21 2017

Sum_{k=1..n} a(k) = c * n^3 / 4 + O((n*log(n))^2), where c = Product_{p prime} (1 - 2/p^2) = 0.322634... (A065474). - Amiram Eldar, Dec 09 2024