A329377 Number of iterations done when n is divided by its divisors starting from the smallest one in increasing order until one no longer gets an integer, or until divisors are exhausted.
1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 4, 2, 3, 3, 2, 2, 4, 2, 3, 3, 3, 3, 3, 2, 3, 3, 4, 2, 3, 2, 2, 3, 3, 2, 4, 2, 3, 3, 2, 2, 3, 3, 4, 3, 3, 2, 3, 2, 3, 3, 4, 3, 3, 2, 2, 3, 4, 2, 4, 2, 3, 3, 2, 3, 3, 2, 4, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 3, 2, 3, 3, 3, 4, 2, 3, 2, 2, 2, 3, 2, 3, 4
Offset: 1
Keywords
Examples
For n = 12, its divisors are [1, 2, 3, 4, 6, 12]. We can divide only three times so that the quotient remains an integer: 12/1 = 12, 12/2 = 6, 6/3 = 2 (but 2/4 = 1/2, a fraction). Thus a(12) = 3. For n = 24, its divisors are [1, 2, 3, 4, 6, 8, 12, 24]. We can divide only four times so that the quotient remains an integer: 24/1 = 24, 24/2 = 12, 12/3 = 4, 4/4 = 1, but on the fifth time 1/6 would be a rational, thus a(24) = 4.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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PARI
A329377(n) = { my(k=n,i=0); fordiv(k, d, if(n%d, return(i)); n /= d; i++); (i); };
Formula
a(A000142(n)) = n.
Comments