A007424 a(n) = 1 if n is squarefree, otherwise 2. (Formerly M0060)

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

1,4

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.

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

Mathematica

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

Prog

(MuPAD) func(2-abs(numlib::moebius(n)), n):
(PARI) A007424(n) = (2-issquarefree(n)); \\ Antti Karttunen, Nov 18 2017

Crossrefs

Cf. A005117, A008966, A107078, A229099.

Cf. A007948, A051903, A130130.

Sequence in context: A194799 A291119 A366309 * A369163 A380398 A323308

Adjacent sequences: A007421 A007422 A007423 * A007425 A007426 A007427

Keyword

easy,nonn

Author

N. J. A. Sloane

Status

approved