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

1,2

Comments

This sequence has similarities with A289280.

Each power of a prime appears in the sequence.

Each prime number appears once in the sequence.

Links

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

Formula

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

Example

For n = 42:
- 42 has 3 primes 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.

Prog

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

Crossrefs

Cf. A000961, A289280.

Sequence in context: A098098 A326066 A080785 * A352047 A245822 A357260

Adjacent sequences: A319602 A319603 A319604 * A319606 A319607 A319608

Keyword

nonn

Author

Rémy Sigrist, Jan 07 2019

Status

approved