

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



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
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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 * A245822 A069797 A158979
Adjacent sequences: A319602 A319603 A319604 * A319606 A319607 A319608


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Jan 07 2019


STATUS

approved



