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

Offset

0

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]));
A369667(n) = ((3==(A003415(n)%4)) && !(bigomega(n)%2));

Crossrefs

Characteristic function of A369668.

Cf. A001222, A003415, A065043, A358773.

Sequence in context: A023973 A297040 A185705 * A358773 A044941 A368699

Adjacent sequences: A369664 A369665 A369666 * A369668 A369669 A369670

Keyword

nonn

Author

Antti Karttunen, Feb 08 2024

Status

approved