A361615 a(n) is the smallest 5-rough number with exactly n divisors.

1, 5, 25, 35, 625, 175, 15625, 385, 1225, 4375, 9765625, 1925, 244140625, 109375, 30625, 5005, 152587890625, 13475, 3814697265625, 48125, 765625, 68359375, 2384185791015625, 25025, 1500625, 1708984375, 148225, 1203125, 37252902984619140625, 336875, 931322574615478515625

Offset: 1

Author

Jon E. Schoenfield, Mar 18 2023

Keywords

• nonn

Examples

			a(1) = 1 (which is the only number with exactly 1 divisor).
a(2) = 5 (since 5 is the smallest prime that is 5-rough).
a(3) = 25 (since 5 is the smallest number that is the square of a 5-rough prime).
a(4) = 35 (since a number with 4 divisors must be either the cube of a prime or the product of two distinct primes, and the smallest 5-rough numbers of these two types are 5^3 = 125 and 5*7 = 35, respectively, and 35 is the smaller of the two).
		

Crossrefs

Cf. A000005, A005179, A007310, A038547.