A007424 a(n) = 1 if n is squarefree, otherwise 2.

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A005117, A008966, A107078, A229099.

Cf. A007948, A051903, A130130.

Programs

Mathematica

Table[If[SquareFreeQ[n],1,2],{n,100}] (* Harvey P. Dale, Jul 09 2014 *)

MuPAD

func(2-abs(numlib::moebius(n)), n):

PARI

A007424(n) = (2-issquarefree(n)); \\ Antti Karttunen, Nov 18 2017

Formula

a(n) = 2 - A008966(n). - Antti Karttunen, Nov 18 2017

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 - 6/Pi^2 = 1 + A229099. - Amiram Eldar, Sep 26 2022

a(n) = A051903(A007948(n)) = A130130(A051903(n)) for n >= 2. - Amiram Eldar, May 07 2024