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

Author

Antti Karttunen, Nov 17 2019

Keywords

• nonn

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

Crossrefs

Cf. A000142, A076933 (final integer reached), A240694.

Programs

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.