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A341994
a(n) = 1 if the arithmetic derivative (A003415) of n is a squarefree number (A005117) > 1, otherwise 0.
7
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
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.
Sequence in context: A011687 A277145 A011690 * A364693 A011688 A144197
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 28 2021
STATUS
approved