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

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

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

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

Cf. A000005, A328308, A328309, A359542.

Sequence in context: A300654 A023157 A228849 * A069733 A187467 A081755

Adjacent sequences: A359538 A359539 A359540 * A359542 A359543 A359544

Keyword

nonn

Author

Antti Karttunen, Jan 05 2023

Status

approved