A329377 - OEIS

%I #12 Nov 17 2019 09:31:48

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A329377/b329377.txt">Table of n, a(n) for n = 1..65537</a>

%F a(A000142(n)) = n.

%e 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.

%e 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.

%o (PARI) A329377(n) = { my(k=n,i=0); fordiv(k, d, if(n%d, return(i)); n /= d; i++); (i); };

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 17 2019