A353495 a(n) = 1 if the arithmetic derivative of n is of the form 4k+2, otherwise 0.

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

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

Formula

a(n) = 1 iff A353493(n) = 2, otherwise 0.

For all n >= 1, a(n) >= A353477(n).

Example

For n = 135, A003415(135) = 162, which leaves the remainder 2 when divided by 4, therefore a(135) = 1.

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A353495(n) = (2==(A003415(n)%4));

Crossrefs

Characteristic function of A327862.

Cf. A003415, A353493.

Cf. also A165560, A353494.

Differs from A353477 for the first time at n=135, where A353495(135) = 1, while A353477(135) = 0.

Sequence in context: A025465 A323514 A369660 * A302047 A044940 A284261

Adjacent sequences: A353492 A353493 A353494 * A353496 A353497 A353498

Keyword

nonn

Author

Antti Karttunen, Apr 22 2022

Status

approved