A076369 a(n) = n + mu(n), where mu is the Moebius function (A008683).

2, 1, 2, 4, 4, 7, 6, 8, 9, 11, 10, 12, 12, 15, 16, 16, 16, 18, 18, 20, 22, 23, 22, 24, 25, 27, 27, 28, 28, 29, 30, 32, 34, 35, 36, 36, 36, 39, 40, 40, 40, 41, 42, 44, 45, 47, 46, 48, 49, 50, 52, 52, 52, 54, 56, 56, 58, 59, 58, 60, 60, 63, 63, 64, 66, 65, 66, 68, 70, 69, 70, 72

Offset: 1

Author

Reinhard Zumkeller and Labos Elemer, Oct 14 2002

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A005117, A008683, A013929, A063015, A076840.

Programs

Mathematica

a[n_] := n + MoebiusMu[n]; Array[a, 100] (* Amiram Eldar, Apr 09 2025 *)

PARI

a(n) = n + moebius(n); \\ Amiram Eldar, Apr 09 2025

Formula

a(n) = n + mu(m) = A000027(n) + A008683(n).

a(n) = n iff n is not squarefree: a(A013929(k)) = A013929(k) and a(A005117(k)) <> A005117(k).