A359542 - OEIS

%I #10 Jan 05 2023 18:30:52

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A359542/b359542.txt">Table of n, a(n) for n = 1..65537</a>

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

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

%o (PARI)

%o 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));

%o A341999(n) = if(!n,n,while(n>1, n = A003415checked(n)); (!n));

%o A359542(n) = sumdiv(n,d,A341999(d));

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

%K nonn,look

%O 1,8

%A _Antti Karttunen_, Jan 05 2023