A336836 Number of iterations of x -> A003961(x) needed before A003961(x) < 2x, when starting from x=n, or -1 if such a number is never reached.

0, 0, 0, 2, 0, 3, 0, 4, 1, 2, 0, 4, 0, 1, 2, 4, 0, 5, 0, 4, 1, 0, 0, 6, 0, 0, 3, 4, 0, 4, 0, 6, 0, 0, 1, 6, 0, 0, 1, 4, 0, 4, 0, 4, 3, 0, 0, 6, 1, 2, 0, 4, 0, 5, 0, 4, 1, 0, 0, 6, 0, 0, 3, 6, 0, 4, 0, 4, 1, 4, 0, 9, 0, 0, 4, 4, 0, 4, 0, 6, 3, 0, 0, 6, 0, 0, 0, 6, 0, 5, 1, 4, 0, 0, 0, 9, 0, 3, 3, 4, 0, 3, 0, 4, 3

Offset

1,4

Comments

Starting from n, the number of prime shifts needed before a term of A246281 is reached.

It holds that a(n) >= A336835(n) for all n, because sigma(n) <= A003961(n) for all n (see A286385 for a proof).

Note that in contrast to abundancy used in A336835, the condition [A003961(x) > 2x] (= A252742) is not monotonic when iterating with A003961. For example, we have A003961(9) = 25 > 2*9, A003961(25) = 49 < 2*25, and then again A003961(49) = 121 > 2*49.

Question: Is the escape clause necessary in the definition?

Links

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

Index entries for sequences computed from indices in prime factorization

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A336836(n) = for(i=0, oo, my(n2 = n+n); n = A003961(n); if(n < n2, return(i)));

Crossrefs

Cf. A246281 (positions of zeros, numbers k for which A003961(k) < 2*k).

Cf. A005940, A252742, A252743, A286385.

Cf. also A246271, A252459, A336835 for similar iterations.

Sequence in context: A115720 A053120 A366601 * A284976 A008743 A029179

Adjacent sequences: A336833 A336834 A336835 * A336837 A336838 A336839

Keyword

nonn

Author

Antti Karttunen, Aug 07 2020

Status

approved