A354874 a(n) = 1 if A003415(n) is squarefree, otherwise 0.

0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

a(0) = a(1) = 0, for n > 1, a(n) = A008966(A003415(n)).

For n > 0, a(n) = A010051(n) + A341994(n), a(n) <= A212793(n).

For n > 1, a(n) = abs(A229343(n)).

Mathematica

d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := If[SquareFreeQ[d[n]], 1, 0]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2022 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A354874(n) = (issquarefree(A003415(n)));

Crossrefs

Characteristic function of A328393.

Cf. A003415, A008966, A010051, A212793, A229343, A341994.

Sequence in context: A358771 A165560 A358220 * A014306 A374220 A335716

Adjacent sequences: A354871 A354872 A354873 * A354875 A354876 A354877

Keyword

nonn

Author

Antti Karttunen, Jun 11 2022

Status

approved