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 A323136 a(n) is the least power of a prime that n reaches under the map x -> A070229(x), or -1 if we never reach a power of a prime. 2

%I

%S 1,2,3,4,5,9,7,8,9,25,11,25,13,49,25,16,17,49,19,25,49,121,23,27,25,

%T 169,27,49,29,49,31,32,121,289,49,169,37,361,169,121,41,49,43,121,121,

%U 529,47,289,49,121,289,169,53,361,121,121,361,841,59,169,61,961

%N a(n) is the least power of a prime that n reaches under the map x -> A070229(x), or -1 if we never reach a power of a prime.

%C The powers of primes correspond to A000961.

%C Apparently, a(n) > 0 for all n > 0.

%H Rémy Sigrist, <a href="/A323136/b323136.txt">Table of n, a(n) for n = 1..10000</a>

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

%F A006530(a(n)) >= A006530(n) when a(n) > 0.

%e For n = 12:

%e - 12 = 2^2 * 3,

%e - A070229(12) = 12 + 3 = 15 = 3 * 5,

%e - A070229(15) = 15 + 5 = 20 = 2^2 * 5,

%e - A070229(20) = 20 + 5 = 25 = 5^5,

%e - hence a(12) = 25.

%o (PARI) a(n) = for (k=0, oo, if (omega(n) <= 1, return (n), my (f=factor(n)); n += f[#f~, 1]))

%Y See A323135 for the corresponding number of iterations.

%Y Cf. A000961, A006530, A070229.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 05 2019

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Last modified October 22 05:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)