The On-Line Encyclopedia of Integer Sequences (OEIS)

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A359541 revision #5

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

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));