A080848 -id:A080848 - cp's OEIS frontend

A080847 a(n) = mu(n)+2, where mu is the Moebius function (A008683).

3, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 3, 3, 2, 1, 2, 1, 2, 3, 3, 1, 2, 2, 3, 2, 2, 1, 1, 1, 2, 3, 3, 3, 2, 1, 3, 3, 2, 1, 1, 1, 2, 2, 3, 1, 2, 2, 2, 3, 2, 1, 2, 3, 2, 3, 3, 1, 2, 1, 3, 2, 2, 3, 1, 1, 2, 3, 1, 1, 2, 1, 3, 2, 2, 3, 1, 1, 2, 2, 3, 1, 2, 3, 3, 3, 2, 1, 2, 3, 2, 3, 3, 3, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1

Offset: 1

Reinhard Zumkeller, Feb 20 2003

Antti Karttunen, Table of n, a(n) for n = 1..5000
Index entries for sequences computed from exponents in factorization of n.

Cf. A008683, one more than A007423, one less than A231821.

Cf. A080848, A080849.

MoebiusMu[Range[120]]+2 (* Harvey P. Dale, Dec 31 2021 *)

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

(define (A080847 n) (+ 2 (A008683 n))) ;; Antti Karttunen, Jul 26 2017

1 <= a(n) <= 3.

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

Original entry on oeis.org

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

Reinhard Zumkeller, Feb 20 2003

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

Cf. A000290, A008683, A080847, A080848.

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

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

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

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

cp's OEIS Frontend

A080847 a(n) = mu(n)+2, where mu is the Moebius function (A008683).

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