|
|
A347245
|
|
Number of iterations of the map x -> A000593(x), when starting from x = n, needed to reach a number whose largest prime factor is at least as large as that of n itself (= A006530(n)). If 1 is reached without encountering such a number, then a(n) = 0.
|
|
6
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,55
|
|
COMMENTS
|
For any hypothetical odd perfect number x, a(x) = 1.
The first occurrence of k = 0 .. 5 is at n = 0, 9, 55, 935, 102753, 262205.
|
|
LINKS
|
|
|
FORMULA
|
For n >= 1, a(n) = 0 iff A347244(n) = 0.
For n > 1, a(n) = 1 iff A347246(n) = 1.
|
|
EXAMPLE
|
For n = 55 = 5*11, on the first iteration we get A000593(55) = 72 = 2^3 * 3^2, but both 2 and 3 are less than 11, thus on the second iteration, we get A000593(72) = 13, which is the first time when the largest prime factor is larger than that of 55 (13 > 11), thus a(55) = 2.
|
|
PROG
|
(PARI)
A000265(n) = (n >> valuation(n, 2));
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|