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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 31 22:27 EDT 2021. Contains 346377 sequences. (Running on oeis4.)