A334098 a(n) = A334097(n) - A331410(n), where former is the exponent of the eventual power of 2 reached, and the latter is the number of iterations needed to get there, when starting from n and using the map k -> k + k/p, where p can be any odd prime factor of k, for example, the largest.

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

Offset

1,4

Comments

Question: Are there any negative terms?

Links

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

Formula

a(n) = A334097(n) - A331410(n).

Totally additive sequence: a(m*n) = a(m)+a(n), for all m, n.

Mathematica

Array[Log2@ Last[#] - (Length[#] - 1) &@ NestWhileList[# + #/FactorInteger[#][[-1, 1]] &, #, ! IntegerQ@ Log2@ # &] &, 105] (* Michael De Vlieger, Apr 30 2020 *)

Prog

(PARI) A334098(n) = { my(k=0); while(bitand(n, n-1), k++; my(f=factor(n)[, 1]); n += (n/f[2-(n%2)])); (valuation(n, 2)-k); };

Crossrefs

Cf. A331410, A334097.

Sequence in context: A188550 A064122 A323424 * A358371 A263922 A057526

Adjacent sequences: A334095 A334096 A334097 * A334099 A334100 A334101

Keyword

nonn

Author

Antti Karttunen, Apr 29 2020

Status

approved