A359542 Inverse Möbius transform of A341999, which is the characteristic function of numbers that will never reach zero when iterated with the arithmetic derivative.

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 3, 0, 0, 0, 2, 0, 0, 0, 4, 0, 1, 1, 2, 0, 1, 0, 4, 0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 0, 2, 2, 0, 0, 6, 0, 1, 1, 3, 0, 2, 1, 4, 0, 0, 0, 5, 0, 0, 1, 5, 0, 0, 0, 2, 1, 1, 0, 6, 0, 1, 2, 2, 0, 2, 0, 6, 2, 0, 0, 4, 0, 1, 1, 4, 0, 3, 1, 2, 0, 0, 1, 8, 0, 0, 1, 4, 0, 2, 0, 5, 2

Offset: 1

Author

Antti Karttunen, Jan 05 2023

Keywords

• nonn
• look

Comments

Question: Why there seems to be frequency bands (horizontal stripes) in the scatter plot?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000005, A328308, A341999, A359541, A359543, A359544 (positions of 0's).

Programs

PARI

A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A341999(n) = if(!n,n,while(n>1, n = A003415checked(n)); (!n));
A359542(n) = sumdiv(n,d,A341999(d));

Formula

a(n) = Sum_{d|n} A341999(d).

a(n) = A000005(n) - A359541(n).