|
|
A165500
|
|
Maximum length of arithmetic progression starting at n such that each term k has tau(k) = tau(n).
|
|
2
|
|
|
1, 2, 3, 2, 5, 3, 7, 4, 2, 5, 11, 3, 13, 7, 6, 2, 17, 3, 19, 5, 7, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Implicitly, we require the difference d of the arithmetic progression to be positive.
a(n) <= n for all n.
|
|
LINKS
|
|
|
EXAMPLE
|
For n=4, tau(n)=3 so each term of the arithmetic progression must be the square of a prime. The difference d must be odd for n+d to qualify, in which case n+2d is even and does not qualify; so a(4)=2 is an upper bound.
|
|
CROSSREFS
|
|
|
KEYWORD
|
hard,nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|