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A353493
The arithmetic derivative of n, reduced modulo 4.
8
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
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);
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 22 2022
STATUS
approved