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A327966
Number of iterations of "tamed variant of arithmetic derivative", A327965 needed to reach 0 from n, or -1 if zero is never reached.
10
0, 1, 2, 2, 2, 2, 3, 2, 3, 4, 3, 2, 2, 2, 5, 3, 3, 2, 5, 2, 4, 4, 3, 2, 3, 4, 4, 2, 3, 2, 3, 2, 3, 6, 3, 3, 4, 2, 5, 2, 3, 2, 3, 2, 3, 3, 5, 2, 3, 6, 4, 3, 6, 2, 3, 2, 3, 4, 3, 2, 3, 2, 7, 4, 3, 6, 3, 2, 6, 5, 3, 2, 3, 2, 3, 3, 3, 6, 3, 2, 3, 2, 3, 2, 3, 4, 4, 3, 4, 2, 4, 3, 4, 4, 7, 4, 3, 2, 7, 4, 4, 2, 4, 2, 3, 3, 3, 2, 3, 2, 4, 4, 4, 2, 3, 3, 4, 4, 3, 4, 3
OFFSET
0,3
COMMENTS
Conjecture: from all n, zero is eventually reached.
LINKS
FORMULA
a(0) = 0; for n > 0, a(n) = 1 + a(A327965(n)).
a(p) = 2 for all primes p.
PROG
(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327938(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]%f[k, 1])); factorback(f); };
A327965(n) = if(n<=1, 0, A327938(A003415(n)));
A327966(n) = { my(k=0); while(n>0, k++; n = A327965(n)); (k); };
\\ Or alternatively, as a recurrence:
A327966(n) = if(!n, 0, 1+A327966(A327965(n)));
CROSSREFS
Cf. A003415, A256750, A327938, A327965, A327967 (indices of the records).
Sequence in context: A147981 A051888 A377014 * A366580 A088019 A301508
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved