A358771 a(n) = 1 if the arithmetic derivative of n is of the form 4k+1, otherwise 0.

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

Offset

0

Links

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

Index entries for characteristic functions

Formula

a(n) = [A003415(n) == 1 (mod 4)], where [ ] is the Iverson bracket.

a(n) = A165560(n) - A358773(n).

a(n) >= A010051(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A358771(n) = (1==(A003415(n)%4));

Crossrefs

Characteristic function of A358772.

Cf. A003415, A010051, A010873, A165560.

Cf. also A353494, A353495, A358773 and A358751 [= a(A003961(n))].

Sequence in context: A286807 A126564 A180433 * A165560 A358220 A354874

Adjacent sequences: A358768 A358769 A358770 * A358772 A358773 A358774

Keyword

nonn

Author

Antti Karttunen, Dec 01 2022

Status

approved