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 A327715 a(0) = 0; for n >= 1, a(n) = 1 + a(n-A009191(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 EXAMPLE a(6) = 1 + a(6-gcd(6,4)) = 1 + a(4) = 2 + a(4-gcd(4,3)) = 2 + a(3) = 3 + a(3-gcd(3,2)) = 3 + a(2) = 4 + a(2-gcd(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

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)