A086700 - OEIS

%I #21 Dec 09 2024 05:28:14

%S 1,2,2,4,8,12,12,12,24,40,20,24,72,48,32,64,96,108,72,48,120,220,88,

%T 80,240,216,108,168,224,240,240,160,320,384,144,216,648,432,192,320,

%U 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

%N Euler phi function applied to the triangular numbers.

%H Michel Marcus, <a href="/A086700/b086700.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A000010(A000217(n)). - _Michel Marcus_, Aug 21 2017

%F 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

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

%p with(numtheory):with(combinat):a:=n->phi(binomial(n,2)): seq(a(n), n=2..31); # _Zerinvary Lajos_, Oct 05 2007

%t EulerPhi[Accumulate[Range[70]]] (* _Harvey P. Dale_, Sep 16 2012 *)

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

%o (Sage) [euler_phi(binomial(n,2)) for n in range(2,32)] # _Zerinvary Lajos_, Jun 06 2009

%Y Cf. A000010, A000217, A065474.

%K nonn,easy

%O 1,2

%A _Jon Perry_, Jul 28 2003