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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.

%I A319605 #44 May 07 2025 12:27:43
%S A319605 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 A319605 27,32,29,32,31,32,81,64,49,64,37,64,81,64,41,49,43,64,81,64,47,64,49,
%U A319605 64,81,64,53,64,121,64,81,64,59,64,61,64,81,64,125,81,67
%N 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.
%C A319605 This sequence has similarities with A289280.
%C A319605 Each power of a prime appears in the sequence.
%C A319605 Each prime number appears once in the sequence.
%H A319605 Rémy Sigrist, <a href="/A319605/b319605.txt">Table of n, a(n) for n = 1..10000</a>
%F A319605 a(n) >= n with equality iff n belongs to A000961.
%e A319605 For n = 42:
%e A319605 - 42 has 3 prime factors: 2, 3 and 7,
%e A319605 - the least power of 2 >= 42 is 64,
%e A319605 - the least power of 3 >= 42 is 81,
%e A319605 - the least power of 7 >= 42 is 49,
%e A319605 - hence a(42) = 49.
%o A319605 (PARI) a(n) = my (pp=factor(n)[,1]~); if (#pp <= 1, n, vecmin(apply(p -> p^(1+logint(n,p)), pp)))
%Y A319605 Cf. A000961, A289280.
%K A319605 nonn
%O A319605 1,2
%A A319605 _Rémy Sigrist_, Jan 07 2019