A343222 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, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 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

1,16

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); };
A343222(n) = if(A003415(n)<=n, 0, 1+A343222(A003961(n)));

Crossrefs

Cf. A003415, A003961.

Positions of zeros: Union of A051674 and A083347.

Cf. also A343221, A344027.

Sequence in context: A376657 A071325 A064727 * A112378 A324832 A035203

Adjacent sequences: A343219 A343220 A343221 * A343223 A343224 A343225

Keyword

nonn

Author

Antti Karttunen, Apr 08 2021

Status

approved