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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.
4
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, 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, 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
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} A328308(d).
a(n) = A000005(n) - A359542(n).
a(n) < A328309(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));
A328308(n) = if(!n, 1, while(n>1, n = A003415checked(n)); (n));
A359541(n) = sumdiv(n, d, A328308(d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 05 2023
STATUS
approved