A343221 Number of iterations of x -> A003961(x) needed until A003415(x) < x, when starting from x=n, where A003415(x) gives the arithmetic derivative of x, and A003961 shifts its prime factorization one step towards the larger primes.

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A343221(n) = if(A003415(n)<n, 0, 1+A343221(A003961(n)));

Crossrefs

Cf. A083347 (positions of zeros).

Cf. A003415, A003961, A343222, A344027.

Sequence in context: A126812 A008442 A338690 * A327169 A299173 A351726

Adjacent sequences: A343218 A343219 A343220 * A343222 A343223 A343224

Keyword

nonn

Author

Antti Karttunen, Apr 08 2021

Status

approved