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

1,1

Comments

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

Links

Table of n, a(n) for n=1..5.

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

Example

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.

Crossrefs

Cf. A075028, A284596, A341213.

Sequence in context: A030244 A004150 A062642 * A363335 A358087 A093484

Adjacent sequences: A294525 A294526 A294527 * A294529 A294530 A294531

Keyword

nonn,fini,full

Author

Jon E. Schoenfield, Nov 01 2017

Status

approved