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

1,2

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

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

Sequence in context: A332334 A217403 A081309 * A010553 A262095 A163374

Adjacent sequences: A329374 A329375 A329376 * A329378 A329379 A329380

Keyword

nonn

Author

Antti Karttunen, Nov 17 2019

Status

approved