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A359541 Inverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative.

%I A359541 #10 Jan 05 2023 18:27:22
%S A359541 1,2,2,2,2,4,2,2,3,4,2,4,2,4,3,2,2,6,2,4,4,4,2,4,3,3,3,4,2,7,2,2,4,4,
%T A359541 3,6,2,4,3,4,2,8,2,4,4,4,2,4,3,5,3,3,2,6,3,4,4,4,2,7,2,4,5,2,4,8,2,4,
%U A359541 3,7,2,6,2,3,4,4,4,6,2,4,3,4,2,8,4,3,3,4,2,9,3,4,4,4,3,4,2,6,5,5,2,6,2,3,6
%N A359541 Inverse Möbius transform of A328308, which is the characteristic function of numbers that eventually reach zero when iterated with the arithmetic derivative.
%H A359541 Antti Karttunen, <a href="/A359541/b359541.txt">Table of n, a(n) for n = 1..65537</a>
%F A359541 a(n) = Sum_{d|n} A328308(d).
%F A359541 a(n) = A000005(n) - A359542(n).
%F A359541 a(n) < A328309(n).
%o A359541 (PARI)
%o A359541 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 A359541 A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
%o A359541 A359541(n) = sumdiv(n,d,A328308(d));
%Y A359541 Cf. A000005, A328308, A328309, A359542.
%K A359541 nonn
%O A359541 1,2
%A A359541 _Antti Karttunen_, Jan 05 2023