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A341994 a(n) = 1 if the arithmetic derivative (A003415) of n is a squarefree number (A005117) > 1, otherwise 0. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A011688 A144197 A295875

Adjacent sequences:  A341991 A341992 A341993 * A341995 A341996 A341997

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 28 2021

STATUS

approved

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)