A353493 The arithmetic derivative of n, reduced modulo 4.

0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 3, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 3, 3, 0, 1, 3, 1, 0, 2, 3, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 3, 1, 1, 0, 2, 1, 0, 0, 1, 1, 0, 0, 2, 3, 1, 0, 1, 1, 3, 0, 2, 1, 1, 0, 2, 3, 1, 0, 1, 3, 3, 0, 2, 3, 1, 0, 0, 3, 1, 0, 2, 1, 0, 0, 1, 3, 0, 0, 2, 1, 0, 0, 1, 1, 3, 0, 1, 3, 1, 0, 3

Offset

0,10

Links

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

Formula

a(n) = A010873(A003415(n)).

For all n, a(4*n) = 0 and a(4*n + 2) is either 1 or 3. [See comments in A235991]

For all n >= 2, a(n) = A010873[(A353496(n)*A353497(n)) + A353490(n)]. (This is essentially Reinhard Zumkeller's May 09 2011 recursive formula of A003415, when reduced modulo 4) - Antti Karttunen, Apr 26 2022

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A353493(n) = (A003415(n)%4);

Crossrefs

Cf. A003415, A010873, A165560, A235991, A353490, A353494, A353495, A353496, A353497.

Sequence in context: A072772 A124314 A059087 * A321932 A321933 A030373

Adjacent sequences: A353490 A353491 A353492 * A353494 A353495 A353496

Keyword

nonn

Author

Antti Karttunen, Apr 22 2022

Status

approved