A319605 a(1) = 1, and for n > 1, a(n) is the least prime power of the form p^k >= n where p is a prime factor of n.

1, 2, 3, 4, 5, 8, 7, 8, 9, 16, 11, 16, 13, 16, 25, 16, 17, 27, 19, 25, 27, 32, 23, 27, 25, 32, 27, 32, 29, 32, 31, 32, 81, 64, 49, 64, 37, 64, 81, 64, 41, 49, 43, 64, 81, 64, 47, 64, 49, 64, 81, 64, 53, 64, 121, 64, 81, 64, 59, 64, 61, 64, 81, 64, 125, 81, 67

Offset: 1

Author

Rémy Sigrist, Jan 07 2019

Keywords

• nonn

Comments

This sequence has similarities with A289280.

Each power of a prime appears in the sequence.

Each prime number appears once in the sequence.

Examples

			For n = 42:
- 42 has 3 prime factors: 2, 3 and 7,
- the least power of 2 >= 42 is 64,
- the least power of 3 >= 42 is 81,
- the least power of 7 >= 42 is 49,
- hence a(42) = 49.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A289280.

Programs

PARI

a(n) = my (pp=factor(n)[,1]~); if (#pp <= 1, n, vecmin(apply(p -> p^(1+logint(n,p)), pp)))

Formula

a(n) >= n with equality iff n belongs to A000961.