A115005 a(n) = (A114043(n) - 1)/2.

0, 3, 14, 43, 100, 209, 374, 641, 1020, 1553, 2246, 3197, 4372, 5911, 7778, 10037, 12728, 16043, 19862, 24467, 29728, 35777, 42626, 50625, 59520, 69675, 80966, 93627, 107568, 123345, 140458, 159673, 180664, 203651, 228590, 255857, 285116, 317363, 352058

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Formula

a(n) = (n-1)*(2n-1) + Sum_{i=2..n-1} (n-i)*(2n-i)*phi(i). - Chai Wah Wu, Aug 15 2021

Mathematica

a[n_]:=2 Sum[(n-i) (n-j) Boole[CoprimeQ[i, j]], {i, 1, n-1}, {j, 1, n-1}] / 2 + n^2 - n; Array[a, 40] (* Vincenzo Librandi, Feb 05 2020 *)

Prog

(Python)
from sympy import totient
def A115005(n): return (n-1)*(2*n-1) + sum(totient(i)*(n-i)*(2*n-i) for i in range(2, n)) # Chai Wah Wu, Aug 15 2021

Crossrefs

The following eight sequences are all essentially the same. The simplest is A115004(n), which we denote by z(n). Then A088658(n) = 4*z(n-1); A114043(n) = 2*z(n-1)+2*n^2-2*n+1; A114146(n) = 2*A114043(n); A115005(n) = z(n-1)+n*(n-1); A141255(n) = 2*z(n-1)+2*n*(n-1); A290131(n) = z(n-1)+(n-1)^2; A306302(n) = z(n)+n^2+2*n. - N. J. A. Sloane, Feb 04 2020

Sequence in context: A291138 A063903 A305009 * A058389 A261481 A059672

Adjacent sequences: A115002 A115003 A115004 * A115006 A115007 A115008

Keyword

nonn

Author

N. J. A. Sloane, Feb 23 2006

Extensions

Offset corrected by Max Alekseyev, Apr 10 2019

Status

approved