A165500 Maximum length of arithmetic progression starting at n such that each term k has tau(k) = tau(n).

1, 2, 3, 2, 5, 3, 7, 4, 2, 5, 11, 3, 13, 7, 6, 2, 17, 3, 19, 5, 7, 11

Offset: 1

Author

Hugo van der Sanden, Sep 21 2009, Oct 09 2009

Keywords

• hard
• nonn
• more

Comments

Implicitly, we require the difference d of the arithmetic progression to be positive.

a(n) <= n for all n.

Examples

			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

Cf. A165498, A165501, A088430.

Extensions

Extended to n=22 (taking advantage of A088430 for n=19) by Hugo van der Sanden, Jun 02 2015