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

1,8

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

Formula

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

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

Prog

(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));

Crossrefs

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

Sequence in context: A047753 A303947 A031123 * A104194 A292261 A035153

Adjacent sequences: A359539 A359540 A359541 * A359543 A359544 A359545

Keyword

nonn,look

Author

Antti Karttunen, Jan 05 2023

Status

approved