A341994 a(n) = 1 if the arithmetic derivative (A003415) of n is a squarefree number (A005117) > 1, otherwise 0.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

Formula

a(n) = [n is composite and A008966(A003415(n))==1], where [ ] is the Iverson bracket.

For n > 1, a(n) = abs(A229343(n)) - A010051(n).

For all n >= 0, a(n) >= A341995(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A341994(n) = { my(u=A003415(n)); (u>1 && issquarefree(u)); };

Crossrefs

Characteristic function of A328234.

Cf. A003415, A005117, A008966, A010051, A229343, A341995, A341996, A341998.

Sequence in context: A011687 A277145 A011690 * A364693 A011688 A144197

Adjacent sequences: A341991 A341992 A341993 * A341995 A341996 A341997

Keyword

nonn

Author

Antti Karttunen, Feb 28 2021

Status

approved