A294528 a(n) is the smallest prime that begins a run of exactly n consecutive numbers having 2, 4, ..., 2*n divisors.

2, 5, 61, 421, 1524085621

Offset: 1

Author

Jon E. Schoenfield, Nov 01 2017

Keywords

• nonn
• fini
• full

Comments

No such run exists for any n > 5; for a proof, see Links.

Examples

			a(3) = 61 because 61 (prime), 62 = 2*31, and 63 = 3^2*7 have 2, 4, and 6 divisors, respectively (and 64 does not have exactly 8 divisors, so 63 is the last number in the run), and there is no smaller number having this property.
a(5) = 1524085621 because the 5 consecutive integers 1524085621..1524085625 have 2, 4, 6, 8, and 10 divisors, respectively (and 1524085626 does not have exactly 12 divisors), and there is no smaller number having this property.
		

Links

• Jon E. Schoenfield, A proof that a(5) is the final term of this sequence

Crossrefs

Cf. A075028, A284596, A341213.