A080849 a(n) = (mu(n)+2)*n^2, where mu is the Moebius function (A008683).

3, 4, 9, 32, 25, 108, 49, 128, 162, 300, 121, 288, 169, 588, 675, 512, 289, 648, 361, 800, 1323, 1452, 529, 1152, 1250, 2028, 1458, 1568, 841, 900, 961, 2048, 3267, 3468, 3675, 2592, 1369, 4332, 4563, 3200, 1681, 1764, 1849, 3872, 4050, 6348, 2209, 4608, 4802

Offset: 1

Author

Reinhard Zumkeller, Feb 20 2003

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000290, A008683, A080847, A080848.

Programs

Mathematica

Table[(MoebiusMu[n]+2)n^2,{n,50}] (* Harvey P. Dale, Sep 02 2024 *)

PARI

a(n) = (moebius(n)+2)*n^2; \\ Amiram Eldar, May 17 2025

Scheme

(define (A080849 n) (* n n (+ 2 (A008683 n)))) ;; Antti Karttunen, Jul 26 2017

Formula

n^2 <= a(n) <= 3*n^2.

a(n) = n * A080848(n) = A000290(n) * A080847(n). - Antti Karttunen, Jul 26 2017

Sum_{n>=1} 1/a(n) = (Pi^4 + 6)/(12*Pi^2). - Amiram Eldar, May 17 2025