A385212 a(n) = n^(mu(n)^2), where mu is the Möbius function (A008683).

1, 2, 3, 1, 5, 6, 7, 1, 1, 10, 11, 1, 13, 14, 15, 1, 17, 1, 19, 1, 21, 22, 23, 1, 1, 26, 1, 1, 29, 30, 31, 1, 33, 34, 35, 1, 37, 38, 39, 1, 41, 42, 43, 1, 1, 46, 47, 1, 1, 1, 51, 1, 53, 1, 55, 1, 57, 58, 59, 1, 61, 62, 1, 1, 65, 66, 67, 1, 69, 70, 71, 1, 73, 74, 1, 1, 77, 78, 79, 1, 1, 82, 83, 1, 85, 86, 87, 1, 89, 1, 91, 1, 93, 94, 95, 1, 97, 1, 1, 1

Offset

1,2

Comments

a(n) = n if n is squarefree, else a(n) = 1.

Möbius transform of A344465(n).

Links

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

Formula

a(n) = 1 + mu(n)^2*(n - 1).

a(n) = n^c(n), where c = A008966.

a(n) = Sum_{d|n} A344465(d) * mu(n/d).

From Amiram Eldar, Jun 22 2025: (Start)

a(n) = abs(A055615(n)) + A107078(n).

Sum_{k=1..n} a(k) ~ n^2 / (2*zeta(2)). (End)

a(p^k) = p^floor(1/k) for p prime, k>=1. - Wesley Ivan Hurt, Jul 02 2025

Mathematica

Table[n^(MoebiusMu[n]^2), {n, 100}]

Prog

(PARI) a(n) = if(issquarefree(n), n, 1); \\ Amiram Eldar, Jun 22 2025

Crossrefs

Cf. A008683 (mu), A008966, A013661, A055615, A107078, A344465 (inverse Möbius transform).

Sequence in context: A182938 A329445 A362248 * A055231 A304328 A304339

Adjacent sequences: A385209 A385210 A385211 * A385213 A385214 A385215

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 21 2025

Status

approved