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

1,1

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

Links

Table of n, a(n) for n=1..10.

Example

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.

Sequence in context: A104024 A339144 A233472 * A216485 A096681 A247793

Adjacent sequences: A284593 A284594 A284595 * A284597 A284598 A284599

Keyword

hard,more,nonn

Author

Fred Schneider, Mar 29 2017

Extensions

Name clarified by Jon E. Schoenfield, Apr 28 2019

Status

approved