A369667 - OEIS

A369667

a(n) = 1 if n' == 3 (mod 4) and n has an even number of prime factors with multiplicity, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415(n).

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

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OFFSET

LINKS

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

Index entries for characteristic functions

FORMULA

These formulas should be computed with a shortcut multiplication, which ignores the right hand side expression if the left hand side yields zero:

a(n) = A358773(n) * A065043(n).

a(n) = [A003415(n) == 3 (mod 4)] * [A001222(n) == 0 (mod 2)], where [ ] is the Iverson bracket.

PROG

(PARI)

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