A323734 a(n) is the largest number j whose n-th power has exactly j divisors.

1, 2, 3, 40, 45, 1, 7, 225, 153, 640, 4851, 6348, 325, 19474560, 1, 976, 18513, 1225, 19, 107747640000, 81, 1, 23, 245790720, 49, 2601, 2133, 3025, 94221, 56241820800, 31, 20063232, 4225, 15262600, 4761, 19236456, 37, 25462407801600, 5929, 2952832000, 21921921

Offset: 0

Author

Jon E. Schoenfield, Jan 26 2019

Keywords

• nonn

Comments

a(n) is the largest (and last) of the A323731(n) numbers in row n of A323730.

If a(n)=1 then n is a term in A323732; otherwise, n is a term in A323733.

Examples

			The numbers j whose 3rd powers have exactly j divisors are 1, 28, and 40; the largest of these is 40, so a(3) = 40.
The only number j whose 5th power has exactly j divisors is 1, so a(1) = 1.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000005, A073049, A323730, A323731, A323732, A323733.