

A327715


a(0) = 0; for n >= 1, a(n) = 1 + a(nA009191(n)).


0



0, 1, 1, 2, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 8, 9, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 19, 20, 20, 21, 19, 20, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 20, 21, 21, 21, 22, 23, 23, 24, 25, 26
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k with k  gcd(k,d(k)), where d(k) is the number of divisors of k (A000005).
Empirically: n/log(n) <= a(n) <= n/log(n) + 2*log(n).


LINKS

Table of n, a(n) for n=0..81.


EXAMPLE

a(6) = 1 + a(6gcd(6,4)) = 1 + a(4) = 2 + a(4gcd(4,3)) = 2 + a(3) = 3 + a(3gcd(3,2)) = 3 + a(2) = 4 + a(2gcd(2,2)) = 4 + a(0) = 4.


PROG

(PARI) a(n) = if (n==0, 0, 1 + a(n  gcd(n, numdiv(n)))); \\ Michel Marcus, Sep 25 2019


CROSSREFS

Cf. A000005, A009191, A155043.
Sequence in context: A036370 A005208 A110007 * A306574 A088527 A030602
Adjacent sequences: A327712 A327713 A327714 * A327716 A327717 A327718


KEYWORD

nonn


AUTHOR

Ctibor O. Zizka, Sep 23 2019


STATUS

approved



