A053047 a(n) is the first (and maximal) power of 2 arising during iterations of the Euler phi function with initial value n!.
1, 2, 2, 8, 32, 64, 128, 1024, 1024, 8192, 65536, 262144, 1048576, 4194304, 16777216, 268435456, 4294967296, 8589934592, 17179869184, 274877906944, 549755813888, 8796093022208, 140737488355328, 1125899906842624
Offset: 1
Keywords
Examples
For n = 10, the initial value is 10! = 3628800 and the iteration chain is {3628800, 829440, 221184, 73728, 24576, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is the 6th element, arising after 5 iterations of phi, and its value is 8192.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..657
Formula
a(n) = 2^A053048(n). - Amiram Eldar, Aug 17 2024