A259846 Number of steps to get from n to 1 by process of replacing with sum of divisors if the result is odd, or dividing by 2 if even.

0, 1, 3, 2, 5, 4, 4, 3, 7, 6, 6, 5, 6, 5, 7, 4, 9, 8, 8, 7, 6, 7, 7, 6, 7, 7, 9, 6, 9, 8, 6, 5, 8, 10, 8, 9, 10, 9, 8, 8, 8, 7, 9, 8, 10, 8, 8, 7, 11, 8, 11, 8, 11, 10, 11, 7, 10, 10, 10, 9, 8, 7, 10, 6, 9, 9, 12, 11, 9, 9, 11, 10, 12, 11, 9, 10, 9, 9, 10, 9

Offset

1,3

Links

Table of n, a(n) for n=1..80.

Example

a(9)= 7 because 9 -> sigma(9)= 13 -> sigma(13)= 14 -> 7 -> sigma(7)= 8 -> 4 -> 2 -> 1, hence the trajectory {9 -> 13 -> 14 -> 7 -> 8 -> 4 -> 2 -> 1} with 7 iterations.

Mathematica

f[n_]:=Module[{a=n, k=0}, While[a!=1, k++; If[EvenQ[a], a=a/2, a=DivisorSigma[1, a]]]; k]; Table[f[n], {n, 1, 150}]

Crossrefs

Cf. A000203.

Sequence in context: A140061 A292776 A061313 * A087669 A053087 A316519

Adjacent sequences: A259843 A259844 A259845 * A259847 A259848 A259849

Keyword

nonn,easy

Author

Michel Lagneau, Jul 07 2015

Status

approved