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 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

%I

%S 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,

%T 27,32,29,32,31,32,81,64,49,64,37,64,81,64,41,49,43,64,81,64,47,64,49,

%U 64,81,64,53,64,121,64,81,64,59,64,61,64,81,64,125,81,67

%N 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.

%C This sequence has similarities with A289280.

%C Each power of a prime appears in the sequence.

%C Each prime number appears once in the sequence.

%H Rémy Sigrist, <a href="/A319605/b319605.txt">Table of n, a(n) for n = 1..10000</a>

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

%e For n = 42:

%e - 42 has 3 primes factors: 2, 3 and 7,

%e - the least power of 2 >= 42 is 64,

%e - the least power of 3 >= 42 is 81,

%e - the least power of 7 >= 42 is 49,

%e - hence a(42) = 49.

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

%Y Cf. A000961, A289280.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 07 2019

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)