A284596 a(n) is the minimum number that is the first of n consecutive integers with an increasing number of divisors.

2, 1, 73, 61, 35521, 11371, 7392171, 168776043, 1584614377, 38045133481

Offset: 1

Author

Fred Schneider, Mar 29 2017

Keywords

• hard
• more
• nonn

Comments

Comment from Giovanni Resta, Apr 02 2017: (Start)

In A075028 the chain has to be at least of length k, whereas here it has to be of length exactly k.

Here a(2) = 1, because d(1)=1, d(2)=2, d(3)=2, so the first chain of 2 starts at 1.

(End)

Calculated with a brute force C++ program.

a(11) > 10^13. - Giovanni Resta, Apr 14 2017

Examples

			61 => 61^1 => 2 divisors
62 => 2^1 * 31^1 => 4 divisors
63 => 3^2 * 7 => 6 divisors
64 => 2^6 => 7 divisors
65 => 5^1 * 13^1 => 4 divisors.
So 61 is the first of four consecutive numbers with an increasing number of divisors. 65 breaks that chain. 61 is the minimum such number so it is the 4th number in the sequence.
		

Crossrefs

See A075028 for another version.

Extensions

Name clarified by Jon E. Schoenfield, Apr 28 2019