OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(A000142(n)) = n.
EXAMPLE
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.
PROG
(PARI) A329377(n) = { my(k=n, i=0); fordiv(k, d, if(n%d, return(i)); n /= d; i++); (i); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 17 2019
STATUS
approved